There's nothing traditional to see here, no gay nightlife nor is there anything gay by day, it's not a pretty place to see and there's no beach. What makes this a possible place to visit on your list is "shopping". Yes, there's plenty of shops of all types and flavors in the resorts but the shopkeepers know your tourists and price things accordingly, they can be pretty expensive.
15 minutes in a cab or 20 on the number 1 bus, you'll stop first at "Centro Comercial Atlantico". This is quite a large shopping center with a nice shop selling designer labels just inside the main entrance, some better known Spanish clothing shops such as Pull and Bear and Zara, lots more to choose from for clothes, sports, duty free, a large Carrefour hypermarket including electrical's section (try not to buy electrical's in the resorts, not worth the risk you'll end up with something dodgy that doesn't work).
After "Atlantico" if you head to the main street behind the center (Av Gran Canaria) you have about 3km of shops, one after the other. Again, this is where the locals/residents go shopping so some good prices. There's a market on each Wednesday morning about 1km past the commercial center. As mentioned, the number 1 bus gets you there or drive up towards the airport and take exit number 28.
