Hi Nomak yes there is a go karting circut, it is just outside Benidorm going towards Villajoyosa, you can get the bus there from the old town and should only take about 20 minutes. I would say the difference between the old and new town is the old town has more shops and Tapas bars and the beach is not as busy, where the new town has more entertainment bars and pubs, but you can walk from the old town into the new town, both parts are good and where ever you stay in Benidorm there is something for everyone, have a great time