Grey and gold
http://www.rugsusa.com/rugsusa/rugs/rugs-usa-marrakesh-trellis/smoky-grey/200SBHAC1D-508.html

Grey on grey
http://www.rugsusa.com/rugsusa/rugs/rugs-usa-perma/grey/200MTVS07A-83011.html

Grey and grey-blue
http://www.rugsusa.com/rugsusa/rugs/rugs-usa-leaves/grey/200CCSA4A-508.html

Just a wee bit of white, so less obvious when stained:
http://www.rugsusa.com/rugsusa/rugs/rugs-usa-moderno-trellis/ash/200HJSAN3D-508.html

Another grey and grey-blue:
http://www.rugsusa.com/rugsusa/rugs/rugs-usa-geometric/duck-egg/200CCSA1A-508.html

grey ikat-ish
http://www.rugsusa.com/rugsusa/rugs/loloi-ly-07/grey/176LY07-26076.html

Busy, hides dirt grey ikat
http://www.rugsusa.com/rugsusa/rugs/momeni-hb-14/denim/126HB14-8010.html

http://www.potterybarn.com/products/tile-border-rug-gray/

I have this rug in my living room. It's very plush, and a little more transitional than modern, but the off-white color might meet your husband's request.

Check out Overstock.com, they have a lot of modern options that are reasonably priced.

This is a thicker pile than it looks. I was just looking at (and touching!) it in store yesterday and while I deemed it TOO modern for the use I was looking for, it could be right up your alley. It comes in grey in store or catalog (not online for some reason) and I've bought a few PB rugs for high traffic (read: dogs) areas and they have cleaned beautifully year after year.

http://www.potterybarn.com/products/scroll-tile-rug-porcelain-blue/?pkey=crugs-by-style&cm_src=rugs-by-style||NoFacet-_-NoFacet-_--_-

Good luck in your search!

PB rugs are wonderful - such great quality.

Not sure what your budget is, but these Gate rugs from Room & Board are stunning.
http://www.roomandboard.com/rnb/product/detail.do?productGroup=19303&catalog=room&category=rm_rugs&subcategory=fl_rugs_wool

http://www.horchow.com/p/Dash-Albert-Rug-Company-Tin-Roof-Rug-8x10/cprod53240004_cat13760736_cat12060731_/?isEditorial=false&index=121&cmCat=cat000000cat000046cat12060731cat13760736

West Elm rugs by Alyson Fox.

http://www.westelm.com/search/results.html?words=alyson+fox+rugs&cm_sp=OnsiteSearch-_-GlobalNav-_-Button

just a little white: http://www.wayfair.com/Bashian-Rugs-Greenwich-Gras-Grey-Rug-R129-GY-HG274-QKD2462.html

http://www.wayfair.com/Loloi-Rugs-Expression-Charcoal-Stone-Rug-EXPREX-02CCSN-LYH1606.html

Above your desired price range, but I have to throw in an Angela Adams. I covet her work.

http://www.angelaadams.com/Adriana.html?optionid=1411

Oh - I haven't seen any of her indoor-outdoor rugs (clearly not the wool you are looking for), but maybe this would work.

http://www.angelaadams.com/Munjoy.html?optionid=999

Megan, your dilemma is sooo familiar to me! I just ordered Flor's Hide & Batik, in Grey. It has the white I require...not off-white or ivory, but white... and should be durable enough to hold up to our dogs' foot pads and stand the test of time in a mostly neutral (and tiny) living room that I rearrange and edit frequently. The grey nicely offsets all our beiges, browns, blacks, and whites, but the pattern isn't so strong that it competes with the pops of color in accessories. It is somewhat more grey, and less brown than it appears on my Mac when viewing from the main pages, but looks like a lighter version of the grey that I see when I launch their FlorBuilder software. I ordered a sample first, then a square, which sat on the coffee table for a few weeks before I committed to 16 squares. Another great thing? If I decide the rug needs to be bigger, I'll just order a few more squares!

check out goodweave.org who has certified child labor free rug links to a lot of really awesome knotted wool rug selections from small carpet artisans that won't break the bank.

http://www.ashacarpets.com/html/Scadinavian/scanmoro_Tozan_C_BlueGray.html

http://www.emmagardnerdesign.com/index.cfm/do/Collection.geometric_graphic_contemporary_designer_rugs

also not sure how much emma gardener rugs cost, you'd have to get a quote, but this may offer a lot of inspiration for a modern grey but no white rug :)

also www.2modern.com has a lot of rugs! Check it out :)

In the mean time or for use in another spot, how about doing an over saturated dye job on it. Fushia or indigo or electric blue. It appears to me that you need a synthetic, easily washed rug.
these are within your price range http://www.homedecorators.com/Rugs/material/173/Synthetic_Rugs/

oooo, i like the last one best!

Synthetic never cleans as well as wool. I have had both and dumped all the synthetic and kept my wool. My sister's stain-proof carpet looks spotted after just a few years and my 15-year old turkish rug which was already used when I bought it looks great.

While I really like some of the rugs linked in the comments, I have to agree with Ryn and say go Flor! I now have two separate Flor rugs and love them so much that I keep brainstorming where I could put another! It seems like the perfect fit for your situation; they carry pretty much every solid color, in a wide range of textures, as well as tons of intriguing patterns. I have a five-tile runner in my hallway that vacuums like a dream, as well as a large area rug in my bedroom that while a warm sandy color, looks brand new after 7 months of use. They are remarkable easy to assemble, and the fact that they ship in smallish boxes as opposed to a long plastic-covered roll is extremely convenient. They have a range of prices and materials, but the majority of their tiles are woven from ultra-tough nylon (though definitely don't feel that way). I just realized this reads like an ad, but I really just love my Flor tiles that much!

I also have to add that if you are wanting a more traditional rug look, don't forget about adding a border! Flor will cut the tiles for you for a small fee into several different shapes. Both of the rugs I mentioned in my previous posts have quarter-tile borders on them, which makes them for me. A border in a solid color is a great way to tie the rug to the rest of your decor, as well.

I just bought an indoor/outdoor area rug for our living room to replace the one that our cats destroyed in two months. It isn't the most gorgeous rug I've ever seen, but it looks much better than you'd think; totally acceptable with our midcentury/IKEA mishmash. It's made from recycled plastic, it's reversable, and you can hose it down to clean it. It's something like this:
http://www.lampsplus.com/products/thom-filicia-saddle-collection-tmf121ab-area-rug__x3998.html

PB Teen has some great rugs. I've had two from them (in my grown up living room) and have been really happy with the quality and the way they've held up. Here are some grey and white options.

http://www.pbteen.com/products/trellis-rug-gray/?pkey=crugs-view-all

http://www.pbteen.com/products/lattice-rug-warm-gray/?pkey=crugs-view-all

http://www.pbteen.com/products/decorator-border-rug-warm-gray/?pkey=crugs-view-all

http://www.pbteen.com/products/mini-dot-rug-grey/?pkey=crugs-view-all

Also I clearly lose because I got so distracted poking around the rugs that other folks suggested that I forgot your no black or white request. Duh.

If you are near Needham, MA, check out:

http://thecarpetworkroom.com/

They have remnants that they will cut/bind into custom sizes.

You can shave the snags off with a razor (like the kind you shave with). That works for pills on sweaters, too. Just a quick fix while you are looking for a replacement.

You can buy a piece of carpet from a carpet shop and have them hem and bind it for you - probably a better option with two dogs, a cat and a baby than spending a bunch of money on a rug that's going to get ruined. Carpet will be harder wearing.

Let us know what you choose! I'm about to purchase a grey on grey rug myself:

http://www.rugsusa.com/rugsusa/rugs/rugs-usa-modern-damask/grey/200FIOCO05-8011.html

I have this marrakesh trellis rug in grey and white : http://www.eatsbydesign.com/contemporary-area-rugs/

But, the grey and gold version is stunning:

http://www.rugsusa.com/rugsusa/rugs/rugs-usa-marrakesh-trellis/smoky-grey/200SBHAC1D-508.html

Good luck in your search!

Wow! I didn't realize my question had been posted! I'm excited to look through all of these and will post again when I find a new rug. Thank you thank you thank you!~Megan