Al Fahidi St in Bur Dubai - haggle the price down for electronics (Dubai Museum is on Fahidi St.).
Then walk a few yards to Meena Bazaar/Bur Dubai Souk (Materials, clothes)
Catch an Abra (at one end of the souk) to cross the Creek, walk into the Spice Souk and then into the Gold Souk.
Walk out of the Gold Souk, towards the Creek, turn right heading towards the sea, find the foot tunnel under the Creek, come out the other side and walk along the Creek back towards Bur Dubai, along the way there are places to eat and the Heritage Village.

That's half a day right there.

If you fancy a pint after that, walk towards the HSBC bank, go past it/behind it, cross the road, over the car park, look right at you'll see the Ambassador Hotel, it has a bar, The George and Dragon - cheap beer and decent pub food.