Purchase a few indoor/outdoor carpet tiles to go under your dining area over the wall-to-wall carpet - easier to clean and replace if they get really grungy.

IKEA has lots of options depending on the measurements of your space: http://www.ikea.com/us/en/catalog/categories/departments/kitchen/10471/

Ikea actually has pretty nice solid wood kitchen islands; I have one that's a version of this one: http://www.ikea.com/us/en/catalog/products/80035920/ They're easy to paint or stain, and they show up on Craigslist a lot (that's where I bought mine). If you're handy, you could install a hinged drop leaf and get bar height stools for sitting at it; otherwise it might be better just to get an island with a built-in dropleaf. For underneath I'd either use AT's beloved Flor tiles, a sturdy woven rug, or a rug in a natural fiber like jute.

I highly recommend this one from "Home Styles." It comes with a stainless or wood top, and sells for $218 - $289. I had one with the stainless top in my last apartment, and my daughter has one with the wood top now. The stainless top can get marred easily, depending on how you use it. It's not the most gorgeous wood (it's rubberwood), but it's a good useful size, easy to assemble. Drawers work well, lots of storage below. If you really want to use it as a dining table, you should find a cart with a fold-down extension for the top. You need to be able to get your knees under the top for comfortable seating for dining. I think these are a little better quality than the carts I've seen at Ikea.

One more thing - if the cart or island has wheels it will be less stable than if is does not. I have a gorgeous John Boos cart that is the main work surface in my kitchen, and I wish I'd got the one without wheels. It's just a little too jiggly when I'm working.

http://www.kitchensource.com/kitchen-islands/hs-5217-95.htm

http://www.homestylescollection.com/Home-Styles-Solid-Wood-Top-Kitchen-Cart-5216-95.htm

I take back my remark about the Ikea carts. The "Stenstorp" models are very sturdy, and the butcher block tops are really nice!

I just realized the Flor tiles aren't supposed to be installed over existing carpet, so scratch that suggestion.

I am actually using the go cart desk from CB2 in red as my portable island. I found mine on craigslist for $40 but even at full pop its reasonably priced. I have a toaster oven, griddle, cutting block, and knife holder with some room to spare.

I like the Go Cart table or desk from CB2, or Flytta from IKEA.

I've had carpet tiles over carpet in a few places, and it works ok - just duct tape the seams, and know that if you roll chairs around a lot, you might need to retape them.

As for carts, all of the above suggestions, or find a table you like and put casters on it. Or stalk rich people until one of them gives you their Aalto tea cart! Love that cart...

I had the stainless steel IKEA FLYTTA and loved it. It was big enough to hold our extra wine glasses, cutting boards, and pots and pans without taking up my entire kitchen/living (open concept) area. Very sturdy and not wobbly, plus it has wheels that you can lock if you want to. Highly recommend!

Floor cloths. Why don't more people know about them? They are really suited to kitchen floors. You can do a search on how to make/paint your own.

Also, +1 @Lemonadefish. I think it's fairly easy, once you find an immobile island, to put wheels on it.

@Yonella, what is a floor cloth exactly? I just googled it and it seems to be a big piece of canvas... am I missing something? I'd think it would slide around on carpet; is it heavy enough to stay put?

@Emilyjumpsin Yes, they are like tablecloths for your floor. I found this link explaining their history. I particularly liked this quote:

"These carpets possess a decided advantage over all others, as they are more durable, and in warm weather much more comfortable, and easier to keep clean, and in hot climates the only kind that are not subject to injury from insects; in winter they may be covered with other carpeting without damage, and the room is kept warmer ..."
New Hampshire Gazette
April 8, 1828

Sometimes things go out of fashion that are still useful. Like cork floors-the perfect flooring for kitchens and baths.

it's kind of funny... the trolley in the photo is an alvar aalto artek tea trolley... worth a couple thousand dollars... not a couple hundred! hope that's not what you had your eye on...

An outdoor rug. Inexpensive, readily available and you can wash them with a hose outside or in the tub inside.