I'd agree with others that I think the only option for diving near-ish Penang is Pulau Payar / Langkawi. Penang Island itself doesn't have clear waters and although I'm sure there are dive sites (as there are on Langkawi Island) it seems like no-one in Penang has set up shop yet. Either way it sounds like its not going to work out for your trip but in case anyone is interested I dived Pulau Payar marine park and also Langkawi island itself both quite recently so will give a quick run-down!
Langkawi Island: To my knowledge there's only one dive shop which dives around Langkawi island itself and that's Langkawi Scuba. They're located on Pantai Cenang and all dive sites are a 5 - 10 minute boat ride away. We went in December and were supposed to do two days of diving with two dives on each day but I got sick and we couldn't do the second day. Visibility was atrocious and there was a bit of a current but it was quite enjoyable anyway. On the first dive we used a buddy line and each held an arm of the dive guide (Wanda) who took us around and showed us sea horses, lobster, frog fish, scorpion fish, cuttlefish and gorgeous soft corals. We then had a packed lunch on a deserted beach before starting the next dive which was much the same as the first. Both dives were 60 minutes long and I wasn't bored as I liked spending time looking at the seahorses, frog fish and cuttlefish in an unhurried manner. I guess its muck diving but in very poor visibility.
Pulau Payar: We did two days of diving with two dives per day. We took an extremely bumpy speedboat ride out to the marine park which took about 45 minutes (I think some operators use a ferry which might be a better bet). The diving was ok although obviously not as spectacular as the east coast. The best dive we did was "coral garden" which had some very pretty coral with no evidence of bleaching, lots of fish but also a fairly strong current. "Lembu Rock" was also quite nice with big fields of unbleached staghorn coral and lots of reef fish. Visibility was quite bad in places, especially at deeper depths (for example at Lembu Rock most of the dive was done at 5m because any deeper than that and visibility went way down). There's a wreck which would have been interesting if we could see more than a few metres. We saw a turtle on our safety stop which was nice. The highlight of the trip for a woman who was only snorkelling (which I wouldn't recommend) was seeing a whale shark swimming round the boat whilst we were 20m below on the wreck enjoying awful visibility! The marine park is not the nicest place and there was lots of rubbish on the surface at some spots. We did two dives each day with an hours surface interval and were either in the dive boat or under the water so it wasn't that comfortable.
I'd say both places are worth a visit if you're in the area, fancy a day of diving and manage your expectations! It's not world class but its perfectly enjoyable and the dive sites are nice and empty which is always good. If you go to Pualu Payar try and sit at the back of the speedboat and also wear sun cream. I neglected to do both of these things and suffered for it.