Just come back from a week in Tenerife over Christmas.
Based myself in a hotel in Los Cristianos, Tenerife. Had a great time. Weather was lovely.
Los Cristianos is a quieter area in the south of Tenerife, short drive by taxi or bus from the airport; close enough to Playa de las Americas if you want a sample of wild nightlife; nice walk down to the port, loads of good restaurants, ferries over to La Gomera for a nice day trip - have lunch - great to see another island.
When I was there I used the local buses to get around. The main bus station is 5-10 minutes walk from most of the Los Cristianos hotels. There is a kiosk beside the bus stops with a very helpful and fluent English speaker and a little tourist office. I went up to the capital, Santa Cruz de Tenerife, for the day. An hour in the bus each way. The drivers are very helpful, the buses air-conditioned and comfortable, and have a screen at the front of the bus showing the names of the stops and where to get off.
I also went to Los Abrigos, along the south coast, lots of great seafood restaurants, and Los Gigantes, up the west coast, huge cliffs, whale watching, great food.
The bus fares are very reasonable. A really nice way to see the island.
In Los Cristianos there are loads of supermarkets to stock up if you go for an apartment, loads of bars and restaurants. Everyone speaks English.
i think you will really enjoy it.