In town? Tune hotel / Sunway / Traders .. lovely food are around 

I won't say "must", but these are the quite "standard" tourist attractions in Penang:

- Penang Hill
- Kek Lok Si temple (can visit this two in a morning, coz both at Air Itam area)
- +/- Thea Kong Thua Temple (near Penang Hill)

- Wat Chaya Mangalaram, aka the Reclining Buddha, aka Sleeping Buddha temple (actually the Buddha's eyes are wide open), a Siamese temple
- Dharmikarama Burmese Temple (just opps the above temple)

- Fort Cornwallis                 
-Khoo Kongsi (a clan house)
- Clan jetties                       
-Cheong Fatt Tze Mansion
- Kuan Ying Temple             
- Penang Toy Museum
- Tropical Spice Garden       
- Butterfly Farm
- War Museum                   
- Snake Temple

Since you are driving, I would recommend a round Penang Island driving trip.  Good for half day or may even stretch till early evening, depends on how many stops you make. (without stops, 1+ hr can finish round the island liao)

Clockwise round island trip:
- From town, first stop, Fort Cornwallis, and the Esplanade.
- Follow Pengkalan Weld and hit Jelutong Expressway, all the way to Bayan Baru/Bayan Lepas.  Visit the Snake temple.
- Next, to Batu Maung, the war museum, +/- the aquarium(sorry, actual name is something blah blah by the jabatan perikanan, I think )

- After that, Balik Pulau town for lunch break.  Try the famous asam laksa and siam laksa at the corner coffee shop, at the old market. (recommend mix asam and siam)  Must try the fresh nutmeg juice with lime.  Buy the preserved/pickled nutmeg, mango, papaya form the market.  May also get the famous Balik Pulau durians, comes in many "brands"...

- Balik Pulau to Teluk Bahang.  Enroute, pass by durian plantations, Titi Kerawang waterfall, Tropical Fruit Farm.

- Photo stop at Teluk Bahang Dam, +/- picnic stop at Hutan Rimba.
- Continue, Teluk Bahang fishing village, +/- Penang National Park - latest addition, a canopy walk.

- Teluk Bahang to Batu Ferringhi. - Butterfly farm, Tropical Spice Garden
- Batu Ferringhi - Tanjong Bungah: toy museum, floating mosque

- Tanjong Bungah - Gurney Drive (hawker stalls start around 5pm) - back to town..