I have a flat in Candas (about 8 miles west on the coast). Gijon is largely a modern city but with several interesting historic bits. My spanish family largely use it for nightlife. It has a great beach but Asturias is not short of those.
But if you like to get around the local transport is great. FEVE is a narrow guage railway. You can get to Aviles (don't be put off by the industrial surroundings - it has a heart of Asturian gold) and lots of places on its network. It's cheap. RENFE (normal trains) can get you to Oviedo quicker than FEVE (Oviedo is well worth a look if you like cities and I think much more interesting than Gijon).
Buses run on time. just go to the office at the bus station and buy a return. Some of the coastal villages out to the east are well worth a visit.
But to get to the many beautiful deserted beaches or the picos de Europe you will need a car.
Yes you can walk Gijon. Wandered most areas and never had a problem anywhere with any body.
Do check out dates of the fiestas. In Candas we seem to have one every weekend in the summer - the bagpipe and the sardine fiestas are my favourites.
Asturians are friendly souls who enjoy cider (more to that than you might think and entertaining), great food, a certain republican independance, and are great to chat to.
Asturias gets a fair amount of rain even in summer but it doesn't last long most of the time.
When you get to the airport the bus which might be hourly (or two hourly) costs 6Es compared to possibly 40Es by taxi. Timetable easily found in the obvious bus platforms.
Have a great time.
