We are thinking about going to cyprus at the end of june. We have an 18 yr old and 11yr old. They love the beach but also exploring.

Any suggestions good or bad, hotels to stay at etc?

Lucky you - going to Cyprus! I have English friends who have recently built a house in Northern Cyprus and can't wait to visit!
My suggestion is that you pop along to your local bookstore and pick up either the Thomas Cook "Travellers Cyprus" ( which I found on a booksale for less than $2) or EyeWitness Travel "Top 10 Cyprus".
Both very handy and informative and a must to take along.
I think Cyprus is fabulous and you will have a super time.

Try visiting www.villasrentcyprus.com
they have a things to do section and points of interest for each area.

Welcome to the Official Website of the Cyprus Tourism OrganisationOfficial site of the Cyprus Tourism Organization. A travel planner to the history, archaeology, cuisine, and cruises from Cyprus to the Mediterranean.
www.visitcyprus.org.cy/

which part you going to Turkish or Greek or both?

For exploring/siteseeing:
Akamas/Polis
wine villages of Limassol region especially Lofou which is particularly pretty.
Troodos and Platres and villages such as Kakopetria
Mosaics and tomb of the kings Pafos
Petra dou Romiou Pafos (Intercontinental Hotel is in this area)
Curium amphitheatre near Limassol
Kolossi Castle near Limassol
Limassol Castle in Limassol
There are couple waterparks on the island

I don't often stay in hotels on Cyprus, these ones are good:

Annabelle in Pafos
Le Meridien in Limassol
Amathus Beach Hotel in Limassol although flanked by hotels on each side, near tourist strip
Four Seasons Limassol (nothing to do with the FS chain)

Beaches
Protaras area, some nice beaches around Pafos (Coral Bay, Peyeia)

We loved Paphos! Wonderful town -with a lovely harbor area, great archeological ruins, good food, and beautiful scenery. We booked several day-trips with our hotel, including a 1/2 day Mediterranean cruise and a jeep safari into the mountain areas.

We have always wanted to go back, but just never have!

We were in Greek part 14 years ago. we stayed in limasol and took some day trips, to Paphos (superb mosaics), to Aya Napa (beautiful beaches and a lot of young people0, to Nicosia (it is the old part of the city), Mt. trodos. We took a night tour, including a folklore show at one big restaurants. this is not a must, as the towns (at least Limasol) has hundred of taverns with live music, dance and good food.

Challenge Baghdatis to a match!

I was only there for a day since it was a stop on a cruise, but I spent that day in Paphos and I would go back in a minute.

PalenqueBob, I thought it wasn't possible to visit both sides of Cyprus. I remember some talk about changing that, is it possible now to visit both sides?

Greek Cyprus invented a whole load of AC wine areas just before they joined the EU. The result is mnay little wineries open for tasting. In particular North of Paphos and heading up to the North west coast are some fun wines and great walking in the National parks up there.

Comandaria is the true grat wine of the Island and comes more or less from the central zone.

Monestries