There might be snow upper in the mountains but the valleys is great in May, as Kamil said. Problably Koscieliska or Morskie Oko would be the best options but it's up to you- there are many nice places in Tatras.
Have a nice trip Lolli.
No they're not the same
Koscieliska valley is in Western Tatras (on local maps: Tatry Zachodnie in Polish, Zapadne Tatry in Slovak) and is easily accessible for anyone, a great easy walk.
Koscielec is a peak in High Tatras (Tatry Wysokie, Vysoke Tatry), a relatively easy scramble in summer (but rather not for first-timers), in May you will need winter gear to climb it.
One more comment (sorry for not mentioning at once) - Morskie Oko is not a summit, it's a lake The idea is, that it is surrounded by many beautiful mountans. There is one more lake bit higher - Czarny Staw (Black Lake). Rysy, the highest mountain in Poland (2499m), is situated there. There is a marked trail to the summit. Bit exposed, but protected with chains. Well, as many other destinations to visit
You should know that Morskie Oko is one of the most crowded place in Polish Tatras What's more, in this valley, tourists go through asphalt route in forest and beautiful views are only in the end of trail. BUT I'm not going to discourage you!