Turkish baths are fab and might be good for the teenagers? Google them. Beautiful original Victorian setting, and really relaxing.
I think the Bettys at Harlow Carr is nicer than the one in town, but both good. My preference for the one in town is to go around 6-7pm, when it's pretty quiet - either go for a drink/cake before dinner, or go a bit later and have dessert/coffee. It's candlelit then, with piano music, much nicer than the hurly burly of the day.
You can walk from town to Harlow Carr - a couple of miles, i think, walking through the Valley Gardens and the Pinewoods, which is very nice.
i had a very nice evening meal once at the 'Harrogate Brasserie' which is a hotel as well.
A really fab place to eat is the Chinese restaurant in the Royal Baths - absolutely amazing surroundings but perhaps a bit on the formal/pricey side. Unique though.
Also, think people have divided opinions on this, but I really like Sunday lunch (or similar) in Hales Bar - very old pub, with gas lighting and the old-fashioned Victorian tiny rooms.
Mercer art gallery is very nice, if that's your thing - small and quick to look around but interesting/individual.
The Pump Rooms museum is good for a short visit - not deeply revealing, but quite small and pleasant. Definitely get the teenagers to taste the (horrible & sulphurous) water - think you can taste it for free from a pump outside, or have some while you visit the museum. On a recent documentary, Michael Portillo said the secret of the success of the Harrogate Spa waters was its high sulphur content which kills off intestinal worms (and according to him, 90% of the population had worms in the 19th century. Nice!)
Umm, that's all i can think of for the moment...