Barbara, I typically refrain from providing restaurant recommendations because it's such a subjective issue, we all have different tastes and expectations and what one may consider good food another would disagree.
However, my last trip to Warsaw was with 6 other friends, we all consider ourselves foodies so based on the fact that we all enjoyed the food I feel that it is a fair representation of the quality. Two of the restaurants that we particularly enjoyed were MOMU (http://www.momu.pl/menu-2) which is close to the Old Town. We ate there for breakfast and enjoyed it so much, and were desperate to try the lunch menu, that we returned a couple of hours later. Fantastic restaurant serving mainly traditional Polish food with a modern touch and some innovative cooking.
Another favourite that we simply stumbled upon one evening was Kuźnia Smaku (http://kuzniasmaku.pl/EN/). This is a traditional 'old school' restaurant in the Hotel Mazowiecka. Excellent food, particularly the duck, and fantastic service. Whilst quite formal there is no dress code, we all rocked up in jeans and t-shirts and no-one batted an eyelid. In contrast there were other diners who had made more of an effort so if you want to you won't look out of place.
If you are beer lovers then a perfect place to visit would be PiwPaw on Foksal (http://www.piwpaw.pl) where you will find over 80 beers on tap and many more bottles. It's a large but busy pub popular with students and young people. Don't worry about trying to pronounce the beers, you can simply ask for a glass by the number of the tap, your only problem will be trying to decide what to go for!