The weather was very hot when we visited Copenhagen so we decided to cool down at the outdoor pool at Islands Brygge Havenbadet near the Langebro bridge.
This pool is open daily from June to September (7am to 7pm) and, best of all, it's completely free. The water is from one of the city's canals and it was "reasonably" clean. It was very cold though, had it not been 27 degrees weather I don't think I'd have stayed in too long.
There are a few different sections to the pool. My favourite was the diving area from where you could jump in from either 3m or 5m up. Scarier than it sounds!
The pool is very popular with locals and a visit here is a good way to relax and escape the heat in the summer.
OK, this isn't California or Australia. In fact it isn't even the rest of Denmark with long, deserted beaches like on west Jutland. But nevertheless, Copenhagen beaches exist and are a great way to escape the bustle of a big city. This picture is from Charlottenlund (and also has a pier bath for adults), which is great if you have children as the aquarium is just across the road, but there are other ones both north and south of the city centre. They also often overlook Sweden on the other side of the strait and you see plenty of pleasure boats. Summertime, a small beach has also been constructed every summer at Islands Brygge, almost in the city centre. Some of the beaches have barbecue facilities so you can bring your own coal and food. In 2005, the beach at Amager Strand, just south of the centre, was expanded with the help of architects and city planning, and now has even more facilities than before (see page below) so that is definately an alternative.
Frederiksberg Swimming Baths has both a large and a small pool, a special pool for infants, a hot-water pool, and a 110 metre-long indoor water chute - as well as springboards, dry-air and turkish baths and a solarium.
I'm sure that you'll definitely have fun there, as I did it many times there! :-)
Equipment You'll have to take all the necessary things with you as to all swimming pools: towel, shampoo, soap etc.