April is in the so-called
dry season, so you should have more chance of sunny, calm days, which will make for good viz and glassy seas. In the TAR park currents are mild to non-existent. Lots of coral, sandy bottoms, excellent macro life - turtles and a variety of rays are not uncommon.
The TAR Park is right on the doorstep of the city - there are 5 islands between 10 and 20 minutes boat ride away from the city centre with a varied selection of dive sites. Quality of the sites vary, but are interesting, especially considering the proximity to the city.
A little bit further away is Pulau Tiga - potentially good for a group - diving is ok, but there's a mud-volcano, which makes for excellent lunch-on-shore entertainment

Mantanani is another popular site, but is a few hours drive.
There are several dive shops in Wisma Sabah, Likas Shopping Complex - there's no dive shops in Sutera Harbour though, just a small Borneo Divers office.
Other operators to consider are Borneo Dream and Dive Down Below - both of which you can find via Google.