Eastbay - take the taxi. A trip to downtown will run about $12, plus a $3 surcharge ($5 from Fri eve to Sun). There's also a 50% surcharge on the meter fare for trips that start after midnight, so you'll probably be hit with that. Trip should be about 20 minutes if in downtown area.

As for what to do... for a day, loads. Little India, Birdpark, the Orchid park at the Botanical gardens, Night safari.