Gordos
Being a bit older I can't advise you on the nightlife but there are a number of nice bars around by the harbour area where the younger Greeks hang out & the Sorrento is just over the bridge at the entrance to the lake almost next to the old Customs office, you can't miss it really. Agios isn't that big that you'll miss anywhere, it's all very laid back & not a haven for groups of Britsabroad. Think of it a as a small provincial resort!
Personally I prefer to avoid the restaurants around the lake as they tend to be very pushy & IMO overpriced. The best I've eaten at there was Okeanos, speciality is fish but again not cheap. Round the back near there is the Pelagos which is one recommended by a friend & also there is a Mediterannean roof restaurant overlooking the harbour above one of the bars, again recommended by a friend & they are probably 3 of the smarter places in town away from the people in shorts. The Strada is good in the town, with an eclectic huge choice (curried risotto anyone?) but some great dishes like a fish carpaccio & lamb with orzo.
Around the walk from the Harbour to the Kitroplateia beach it's pretty well wall to wall restaurants. Mourageio & Crysambelos (anglicised spellings) are 2 nice meze style places & the last one on the stretch before the marina is called Ofou To Lo run by my friend Antonis, which is a pleasant place to chill out (try the lamb special stuffed with cheeses!). To be honest, speaking to 10 people will get you 20 recommendations! I try to look for places the Greeks are eating in.
If you fancy getting out there are a number of places to eat in Elounda but my favourite over that way is Giorgios's at Plaka, the middle of the 3 restaurants which overlook Spinalonga island, the old leper colony. It is always full of Greeks, particularly at the weekends and Spiros & Yiannis always make people welcome and a wonderful view.
Going the other way Istron has a few decent place Istron Taverna, Zygos & the newly reopened Pelagos. For cheaper meals we head into one of the hill villages but that can be hit & miss, but lovely anyway. Make sure you have the snails, cuttlefish, octopus etc & we find eating like the locals with lots of smaller dishes is far more pleasurable.
There are a number of car hire companies around the harbour area, Economy as mentioned, Byron, Kerai so you'll not have a problem. Along the coast is an excellent bus service as well & (what they call) the bus station is up the hill by the hospital.
As for beaches, there are a couple of small ones in & around town. Almyros is excellent & about a 20-25 min walk along the road past the little football ground. Elounda has a reasonable town beach. Plaka a very pebbly one at the far end. Again Istron has 3 reasonable beaches & if you want to travel then there's Tholos, over at Kavousi is pebbles all the way but only a few people (about 15 when we wre there in July), & down at Makrigialos on the south coast is nice.
Hope that helps & have a great time.
Pete