In reply to BuckoBoyle:
April is still full winter in the mountains , and axe / crampons will be essential for anything but the easiest stroll to one of the huts.
Its been quite a snowy winter and has been snowing heavily in the mountains for days.
Current avalanche conditions and webcams can be seen on the link below.
The Slovak side is well worth a visit , and something like 80 % of the Tatry are in Slovakia.
Its worth noting that the Slovak side closes its trails ( above the huts) for general hiking all winter ... till early june
Make sure you have insurance/ id card at all times , as its a regulation of the park...but it is rare to be asked ( especially on the Polish side)
All winter equipment can be hired at Kuznice before the cable car station to Kasprowy.
In general the Tatras pack a punch for there size , and bad weather , lots of snow and avalanches are very common.
Saying that...spring can be amazing , and have amazing sunny weather and a stable snow pack.
If you ski?..Kasprowy can be amazing in april..well worth a day up there.
Morskie oko and Zelene Pleso are both amazing , but trails above the huts will require experience in winter as mentioned.
If your only in the Tatras for 3 days i would base yourself in Zakopane , and just do day trips from there...as its a small mountain range.
Zakopane has loads of restaurants , bars and places to stay.
Its worth mentioning ... dont be fooled into looking on the map and thinking the " red path" will an easy stroll to the next valley/ hut..... it could well be a steep ski descent till early june!
If you want i will email you a few ideas for general hiking/ easy peaks.
Oh and dont be put off when you read the park rules in the link below.
http://www.topr.pl/
http://www.tanap.org/national-park-rules/