As no one else has yet answered I'll give you the "benefit" of my rather limited experience.  I've walked from Stary Smokovec to Teryho chata (chata means hut, I think) and from SS to Zbojnicka chata.  Both good day walks and you can get lunch/beer/hot drinks at the huts.

A hurricane went thru the southern side of the Tatras a few years ago so be prepared for scenes of devastation at lower levels.  Once you get above about 1100m things are OK.

The map of the mountains is available here:
Link

You could even walk across to Zakopane (and catch the bus back, or vice versa), if you have the time.  You'd need to take your passport if you did this, though.

Edit: Trevor and AN Other got in whilst I was writing my reply!

Thanks All,

I've ordered the Ciccerone guide, and am off to Stanfords this weekend to get hold of the walking maps. As for the tics, I've forgotten that they'd been a problem in Slovenia as well, so I'll make sure that I pack the tic remover What was the food like? Apparently there's a 24 hout Tesco in Poprad now, so we'll stock up on the day that we visit Aquacity!

It is 9 years since we went (1999)  there and I am sure lots have changed, but we went in August and it is quite busy. The huts were full so we stayed just outside Stary Smokovec and used the local tram / train system to get around.

These trains used to be full at 08:00-08:30 in the morning, and if my memory is correct the timetable was a bit erratic.

 The place was cheap though, 2 of us used to have meal and a couple of beers for £5 between us.

 As far as walking is concerned in those days you were restricted to the way marked trails unless you had a guide or were a member of a mountaineering club. Never did work out what the definition was, but found the trails gave us more than enough to play with for 10 days.

Some of the routes had fixed chains on them, supposed to be one way but..... very interesting.

Weather was generally good though the odd late afternoon storm was entrtaining.

I am sure you will enjoy it.

Flying to Poprad is good, we flew to Prague and then got an overnight sleeper, also in those days you needed Crowns as currency, cheque, Slovakian, plus we had some DM, $ and £ with us, though is it now Euros.

Dazz wrote (see)

, also in those days you needed Crowns as currency, cheque, Slovakian, plus we had some DM, $ and £ with us, though is it now Euros.

Thought it was still Slovak Crowns check rates here

Fond memories of Teryho chata, well worth a stay.

A few years since I was there as well, was certainly cheap to stay in the High Huts (chata's?) and the food was good. I managed to get in the huts without big problem, but I was walking by myself and the Tatras weren’t particularly popular at the time, I should imagine you'd have to book now, but if you can get in, do so, loads of atmosphere.

The restricted walking’s a bit of a pain, but that shouldn’t really become a problem on a first visit.

Flying in to Poprad, you’re missing one of life’s (Michael) Palin-esk type train journeys - or it was anyway – great big trains rumbling through the night, strange drunken men bursting into your carriage in the middle of the night and bending your ear in a language you can’t understand, border guards demanding your passport and shining torches in your face – also in the middle of the night ~ arr the romance of it all. Possibly slightly tempered by the fact you’re not quite certain you’re on the right train and can’t speak the inebriated lingo to check and so are very relieved when you see the Poprad sign next morning.

Hayley Dyer 3 wrote (see)

Aye the currency is Koruna rather than Euros. Sky Europe are having another sale this coming weekend if anyone else is interested in flying to this part of the world!

Sky Europe certainly are ones to watch for cheap air-fares, earlier this year I booked a return to Bratislava in October for £20. Definitely worth signing up to their mailing list.

Take a few Zlotys with you aswell if you fancy doing a bit of border-crossing into Poland.