The rail system is great for getting around the various drop off points for walking. There are lots of accommodation options in and around the rail network, plus there are high huts if you want to walk up and stay high.
The high routes open on June 15 or later if the snow is still abundant. I spent a few days there in late May 16 and although the high routes weren't open there was plenty to do. Bird wise there is little in the way of reserves with hides but we had no trouble seeing lots from the trails. Nutcracker was plentiful right down to the resorts.
Park rules http://www.tanap.org/national-park-rules/
Good online map https://mapy.hiking.sk/?ref=navigator
Where we stayed https://www.holidaylettings.co.uk/re...-strba/1774533