Both beaches are great, really sandy and with good swimming. I personally prefer the beach on the right as you look out to sea from the harbor. As you are staying at harbor you are right in the middle of the two beaches.
For food we generally wander up and down the front looking for the place with the best menu del dia. The menu is served at lunch time and is usually much cheaper than the rest of the food on the menu. The restaurant owners in Calpe don't seem to advertise them well and there is usually a small printed sign on the front of the restaurant or a blackboard. It is normally only in Spanish, so take your phrase book if you need help in Spanish. On the sea front nearest to the old town there is a nice little place that serves 12 sardines and glass of wine for 5 euros. They also do other tapas food, a good place to go for a snack. On the other beach, at the end furthest away from the harbor is a good Italian we have eaten in a number of times, but it wasn't that cheap. If you have a day wanting really cheap food there is a Chinese just behind the harbor which is just like all the other chineses in Spain, very very cheap, but alot of food, not that great but good for a cheap night out. If you want to splash out there are fish and sea food restaurants in the harbor. If you love seafood they are wonderful. Food is shown in cooler cabinets at the front and the atmosphere is wonderful. It would be a good idea to book if you want to go for Sunday Lunch, they get really busy. Waiters come out the front with food and Sangria to try and get you to go.
Trips out
You can climb up the inside of the Ifach, the big rock. It's a bit of a climb, but the views are wonderful once you get to the top. Get there early as numbers inside are limited and the tickets are free.
Boat rides round to the other coastal towns, Javea is nice, 2 beaches. One sandy with loads of cheap restaurants down the front. The other beach is shingle and has a lovely old town with trendy cafes. We often eat at the indian on the front in the old town. It has an orange sun shade. Javea is very Spanish, I work at a private school in Valencia and all the kids in my class have a beach house there.
Moriara is nice too, a bit smarter and quieter than Calpe with good beaches.
We went to Benidorm the other day, we were surprised how nice it was, however we did go during a Spanish bank holiday weekend and there were no brits there at all.
There is the big theme park Terra Mitica. i've never been, but friends with teenagers say its good. I think there is a free bus from Calpe. The tourist information is in the harbor area so you could ask there. There are also water parks, again I think there is a bus there.
There are also day trips to Gualdalest. I've been up there twice, with two different sets of visitors. Not much there, but there are good views and a castle to walk round and a few restaurants. If you go the first restaurant as you get to off the bus was lovely. Outside it looked like it just served burger and chips, but we went inside and they did a wonderful cheap menu del dia.
Sorry I don't play tennis so i don't know about courts.
We live in Valencia, but often go to Calpe for short holidays and days out. We were there for a long weekend last week. First holiday for DD who is 11 weeks. I love it there! Have a wonderful holiday.