Two hugely attractive targets in Warsaw require no "tour" booking or such - just go and enjoy on your own. You can do both in one day, easily, and it will be a very memorable day for you.
1) Chopin museum (www.mydestinationwarsaw.com/things-to-do/fryderyk-chopin-museum-in-warsaw - closed Mondays). Frederic Chopin is one of Poland's absolute folk heroes (as is Kopernicus!), and even if you're not a classical-music buff, don't miss the museum. The large video displays and other exhibits are fascinating in the way they bring to life cultural and even political history, and whenever you get "museum feet", sit down at one of the many listening stations (with headphones) on the lower floor and indulge in some Mazurkas or Polkas, that will put a pep into your step in no time.
From there, a very short walk away you can pick up the bus that runs along the north-south artery of Aleje Ujazdowskje (ask the attendants at the museum for the bus number, I can't recall it right now) that takes you to
2) ?azienki Park (Polish: Park ?azienkowski or ?azienki Królewskie, details at www.mydestinationwarsaw.com/things-to-do/lazienki-park---the-royal-bath), a wonderful large public park full of trees and ponds and - the main attraction - a number of "royal" buildings, some of which are outfitted like museums and open to the public.
The only mildly tricky thing about this is where and how to buy the bus ticket, not every stop has a vending automat since most people have a weekly or monthly card. So ask at the hotel or take a taxi.