The grand park is in Lapad, It's about a 15 minute
Walk from the "Stari Grad" Old Town, during the day the buses are every 5/10 minutes and a little less frequent at night.
The Taxis are cheap anyway and all the hotels have cab numbers, and its a five minute cab ride from Lapad to the Old town.
As for the evenings, it depends what your after!!
The Stradun and the streets off it have some good bars,although its mainly restraunts, a goodplace to go for drinking is Bourbon Street which is a street which runs off the big hill that goes towards the old town (nearly opposite the hotel belle view) there you will find 6 or 7 bars all next to each other, And you can have a good night down there, Its funny that bourbon street never really gets mentioned on this forum?
There is a nightclub opposite the bus station, years ago it was called Sun City, and me and my mates have always called it that since, however it has changed names a couple of times since.
I've not been to Dubrovnik for 18 months or so, but I've heard that a couple of other clubs have sprung up, I'm going in the last week in July, first week in August so I'll let you know via here.
The Hotel Kompas is a good reasonable priced hotel in Lapad (just up from the Grand Park) that has a swimming pool, the hotel Vis is ok but doesnt have an outdoor pool, however it does have its own private beech (shail not sand) which is good.
If you've got any more questions about dubrovnik, just drop a post on here and I'll try and help, Me and my mates have been a good few times to Dubrovink and always enjoy it, infact I'd say Dubrovnik is by far my favourite holiday destination (closely followed by Rovinj) and we're only young lads, but if its a brash spain type holiday your looking for then look else where, but if your looking for the best of both worlds, where you can chill out with very nice friendly people, with top weather and great food and a good drink then dubrovnik is defo the place to go.