Also, is there a good/reasonably reliable transport system (metro or train) from the airport to the city?

It depends on where you're going. Taxis are cheap in the daytime. A taxi from the airport to my hotel across the river from old town was about $20 with tip. It would be less to the Old town.

One of the really good things I did was the Warsaw Uprising Museum. You would definitely need to take a taxi here as it's out of town, located in a disused power plant. You could spend about 2 hours here (or less). When we left there was a taxi outside the main door.

Then go to the old town and walk around and have some lunch and see the palace if you have time and inclination. I didn't see the palace as I've seen so many of them.

There are plenty of taxis near old towns square to take you back to the airport. If you only have 7 hours I don't think you'd want to depend on public transportation.

I agree with our other posters. Plenty of time to get a feel for the reconstruction of the old town. I felt they did a masterfull job. So a little more information. www.inyourpocket.com/Poland/Warsaw and http://en.wikipedia.org/wiki/Warsaw

We loved Warsaw and stayed there two nights at the beginning of our trip to Central Europe. In Warsaw we really liked the combination bus/walking tour. Mazurka Travel has a 3 1/2 hr. morning group tour: http://localtours.mazurkas.com.pl (then click on English, offers, & regular sightseeing of Warsaw). A wonderful restaurant in Warsaw is Podwalk Kampania Piwna.

Thanks everyone. Still looking for specifics about great food and drink if anyone has it.
And, adrienne - I had to chuckle at your comment about a taxi that costs $20 being "cheap"..... it's really a perspective thing I guess. I'm so spoiled. I live in Cairo Egypt, and for $20, I could travel completely acorss the city - probably from the airport to the pyrmaids or further, which would take no less than an hour in traffic - probably more. LOL Having lived like that for the 14 yrs makes me a bit of a cheap-skate.

I don't have any great restaurant to recommend but need to caution you that wine in Poland is quite expensive, not compared to standards at home but compared to Polish prices.

If you lived in the NY metro area $20 for a taxi would seem cheap! The Warsaw airport to my hotel took about the same amount of time as from my home to Newark airport and was a quarter of the price!

Maybe other than trying a Polish glass of wine or a beer, I'll probably stay away from alcohol while there. Gotta be sure to be back to the airport in time for my flight out. Besides, flying on LOT should offer me Polish wine with dinner, shouldn't it?

If my memory serves me right, there is a restaurant called "Pierrogeria" shortly before the Barbacan with quite spartan interior but very nice pierogies. Cah only. "Zapiecek" are I think chain restaurants,I think I saw a couple of them. I visited the one near Castle Square, it is located on Swietojanska if my memory serves me right, and it has a traditional decoration and plates and cutlery,waitresses are dressed accordingly on specific uniforms. Seems a bit touristy but I've seen many locals among visitors too. On main street Krakowskie Przedmiescie there are many restaurants and fast food corner shops where you can find canapetki "sandwiches". There is a beer house too called BrowArmia.
I visited a year ago, so a local might be able to correct me if necessary.

Sounds good mariha2912 - I'll take that info with me and check it out.\
Also started thinking - are their stores in Warsaw a shopping deprived American might find something she didn't know she needed? I'm thinking Marks and Sparks or other like that, or I could be in need of a pretty crocheted or needlepoint type single bed bedspread. Do Polish women do that?