For me the Old town square is a must see in Warsaw for sure. And if you are looking for a place to have a drink and eat something nice you should visit Bubbles It is amazing, cozy bar in the Old Town, with champagnes, wines and drinks, as well as delicious food. Their tomato tartare is insanely good! 

A good idea for a day or morning is to have a walk in Park "Łazienki"and afterwards head to plac Zbawiciela where you can find Charlotte as well as some good Asian food as in Quê Húóng or Tuk Tuk. In that area you can also admire great comunist architecture.

Bar Warszawa de Luxe is open 24/7. I think they even have dance parties there, but I haven't been. The Platinium Club & Restaurant is amazing, but not cheap!

If you are looking for a nice place for a dinner I would definitely recommend the Restauracja Akademia You can try delicious Polish cousine as well as modern European dishes there. The atmosphere is also incredible - elegant but cozy at the same time. For me it is one of the best places in Warsaw!

Try to visit meldunki restaurant. The meal there is really great and the prices are good.

There is a very nice restuarant in the park - bit of a treat as its quite expensive and perhaps in this weather the gardens won't be as brilliant as at other times of the year.  Cant remember the name alas