funkola,
As Mir said I've just returned from Cherkassy so perhaps I can give you some "sketchy" info for a start. Sorry it's only sketchy though... I wish I'd had more time to look around while I was in town.
Firstly it's a small city (pop. 380,000) and appears to be quiet but my friend and I had a lovely time over the weekend.
The Cherkassy Museum of History is definitely worth a look and we spent almost 5 hours meandering through the building looking at exhibits.
If you're going soon you'll also be in a treat if you go down to the Dnipr River and a park that sits on the bank close to the main bridge into town. I've attached a pic but it can't convey the beauty in the area. If you go there on the weekend you'll have a great time watching families and young couples enjoying the park.
There are many old buildings that you'll find on your walk through town and I found this to be a very nice way to pass time with my friend.
Restaurants:
We went to a traditional Ukrainian restaurant in the centre of the city which was excellent and very affordable. My friend organised the reservation so unfortunately I don't have the name but it was housed in a traditional Ukrainian home that was circular and had a courtyard in the middle. We had a 3 course meal and drinks and the bill came to about USD$25-$30. The food was VERY good and on the Friday night there was some live music which created some good "people watching".

There's also a Georgian Restaurant on the outskirts of town (I think to the north just at the start of the pine forests) which we tried to get into but we didn't have reservations so we couldn't get in - BUT the aroma was spectacular. It's a 20UAH-25UAH cab ride away but my friend regarded it as the best restaurant in town so it should be well known... Your friend might know of it! The rest of night all I could think of was THAT smell. If you get there I'd be very interested in hearing your review.
We ended up eating in the hotel that night and had a few good meals there. It's a shame the restaurant doesn't have a view of the outside (It's more like a dining room) but if you're staying in the Dnipr Hotel you'll enjoy the food there (Except maybe for breakfast - which was average). If you eat a big breakfast usually you might be better off walking into a cafe in town (Of which there are a few excellent ones). The prices for food and drinks in the hotel was very reasonable (Dinner and drinks for 2 people was about USD$25 and the food was very good.)
If your friend is picking you up she'll probably suggest getting the bus back to Cherkassy. I got the bus back from Cherkassy to Kiev and thought it was a good option but heed the warning of others and be careful with your valuables.
If you've got any other questions feel free to ask. It might trigger my memory.
I was a little disappointed I didn't spend more time in Cherkassy because by the Sunday I was feeling like I would have liked to stay there for a few more days to continue to get to know the city but if you're having an extended stay you might struggle.
It was a very pleasant stay though. I hope things work out for you and your friend.
Oh, I'll add one thing... When you meet the girls I would not initially assume they are scammers. Assume they are genuine but be wary at all times because bad stuff has happened to others in the past. If your girl is picking you up from the airport she's obviously thinking about your trip and how to make it easier and more comfortable for you. Just be sensible when dating. I don't think you'll find any restaurants in Cherkassy that are outrageously expensive so it'll be difficult to spend a fortune on dining out. Hopefully you'll get an invite to her family home for dinner.
Have a fantastic trip... I'm sure you'll have a ball!
Cheers,
Kuna
The pics:
1. From the park across the river and towards the main bridge into town
2. The War Monument is HUGE and you really can't get an idea of the scale in this photo. You have to walk towards the monument to get to the Museum and it's located just on the right of where this photo is taken.
3. A lovely little church that's in the same area of town.