Hello,
I actually just got back from Mestia today. It was very warm - I got a sunburn everywhere (including my shoulders because I was wearing a tank top!). You should do the day trip from Mestia to the Cross and then to lake (although when we got to about 400m passed the Cross, the earth was covered in snow, so maybe wear proper shoes). It's definitely worth it. Stay that night in Mestia and then take a 7am marshutka to Batumi. I'd take the bus to Sarpi - they have some rocks where you can jump off of into the Black Sea (it's really beautiful, and still warm. I did that maybe two weekends ago). Head back into Batumi and grab some food (in my opinion, it was the best non-Georgian food I had). Then maybe take the night train back to Tbilisi (get a sleeper, so book in advance. Train leaves around 10pm and gets to Tbilisi between 7-8am). From Tbilisi I'd take a day trip to Gori (marshutka or train cost 4lari). If you take the earliest train (say 8am), you can get a taxi to Uplistsikhe for about 10lari, which is one of the oldest cave city's in Georgia. You can walk around for maybe two hours, then take a marshutka/taxi back (make sure you make arrangements for this on the way there or you'll be stranded!). Walk around the Gori fortress and then go to the Stalin Museum (it's really awesome). Take the 7pm train back to Tbilisi.
I'd recommend either Old Town Hostel (the staff is awesome) and it's clean for a min of 20lari (depending on the room they have available, could be as much as 35gel) or Sleep Inn Hostel (which is off of Rustaveli). It's not as clean, and there is only one bathroom, but you're sure to meet really cool people!
Definitely take a day trip to Mtskheta and Davit Gareja.
If you have time maybe a trip to Borjomi National Park (just do a one day hike) and either camp in the park or get a hostel in the city of Borjomi.
In Tbilisi, good night life is the Beatles bar, Cafe Gallery, Club Unique (it really depends on your scene). But if you're in old town and walk down shardeni street you're bound to find something (kind of over priced but very nice bars, lounges, hookah bars, clubs, restaurants, etc).
I recommend taking the gondola up to Queen Nana (get to the lift by walking the peace bridge) at night! It's beautiful. There are also some sulfur bathes (you can get a private room for 20gel). Extra for towels, massages and scrubs (pass the massage and get the scrub if you go!)
