Warsaw is a reasonable base for day trips, though distances in Poland mean you often need a full day for anything worthwhile. Kraków is 2.5–3 hours by train and can be done as a long day trip, though it rewards an overnight stay. The Białowieża Forest (4 hours) — one of Europe's last primeval forests, with free-roaming bison — is more comfortable as an overnight. Mazovia's countryside around Warsaw is accessible by local train for a half-day walk or cycle.
Żelazowa Wola, Chopin's birthplace about 50km west of Warsaw, is an easy half-day excursion by train and bus — the house is set in a beautiful garden where Chopin concerts are held in summer.