If you search "Kiev" in the Trip reports section you should find lots of ideas on what to do and where to go... It's a well traveled location.
If it's your first trip to FSU there will be nothing like it... you just can't imagine how fabulous it is to arrive and experience the things you won't imagine or anticipate.
You need to go to Andrewevshi (sp?) just down from the Golden Domed Cathedral... great little area and an outdoor art gallery (selling is the goal - not exhibiting) that's worth a look.
Sopia Cathedral is also close by...
Lavra is a MUST!
Don't eat at O'Briens - the food is terrible but it's worth dropping in for a few pints one night if you're craving some expat contact... Live music on Friday nights and the expats will give you the run down on what to look out for...
Be careful on the Metro... pick pockets are common...
Chateau restaurant is worth a look and their beer (brewed in-house) is worth a sip.
Arena is a definite night out... I think there's live music there on Thursdays... food is good... beer is well... beer... any single girl sitting in there is a hooker... and not very good looking either...
Strolling down Kreshatic and popping into anywhere that looks interesting is OK and then just start moving further out as your confidence grows.
I think most would go to River Palace for a night out but be aware that any single girl there is probably a hooker... some beautiful girls but I'd stay away from the hookers... can only be trouble.
Museums everywhere - depends on what you want to see... the water park is also worth a look I've heard but I was there in winter and didn't go...
Be a little careful walking around alone late at night... especially if you're drunk. I felt safe in Kiev but there will be dangers in any city of that size - especially when you don't speak the language.
How long are you going for???? What is the purpose of your trip? More tourism than anything??? If you do meet women while there and are well informed they will be impressed because I imagine many men turn up and don't even think to learn a little about the city before arriving.
There's 'What's On in Kiev" books available (look in O'Briens) that will give you some more ideas.... also check out the Kiev post... you might find a copy of "The Best Of..." and that will give you great ideas.
Under Independence Square there is a huge underground shopping mall but Kiev isn't a cheap place to Shop....
Try out some local restaurants and some of the local food... a MUST DO in my opinion! Blini, Holubtsi, Agroshka, Solyanka... Mmmmmm... must be nearly lunchtime!
Take long walks... carry your camera... try to blend in but don't be afraid to say G'day if someone really grabs your attention.
I had a very cool experience with a phone card seller on the street who took me for a vodka in a bar in the metro stop at Independence sdquare. Nice guy... a bit rough around the edges. Invited me home to his place for dinner one night but I didn't trust him enough to go... God knows what might happen but if you step out of your comfort zone just a little you'll have a ball!
The single most important thing you can do while in Kiev is to find an Internet Cafe and post a trip report everyday... that way we all get to relive our first trips...

... but seriously... I got good advice on my first trip when I was posting my TR and it's reassuring to know you've got a few thousand mates at RWD who are willing to help out if required.
have fun!
Kuna