Me and some friends have been playing quite a bit of tennis recently (before the start of wimbledon too).
We pay £3.60 evertime we use a court at graves park (not the tennis and leisure centre) but obviously this can only be utilised during the summer period.

What we're after is some sort of club where can play on good indoor courts (and outdoor weather being dry) for cheap/free if we pay a membership fee.

Now Graves Tennis and Leisure Centre costs the general public £10 per hour for an indoor court and me and my friends normally play for 2+ hrs.
I haven't enquired about a membership (or even if they offer this).

Does anyone know of any clubs which might suite our requirements?

There's one tucked away on the corner of Victoria Road at the Ecclesall Road end. You don't see them unless you look over the wall. 4 courts recently re-laid. Don't know what membership fees are but am sure someone would tell you if you popped down there.

what about Millhouses? Dunno what the situation is there for cost or out of season use but might be worth checking out as there is usually one court free.

millhouses park is free but lacks proper facilities

i live nxt to abbeydale sports club - its about £100 a year membership so if ur serious (get practice in quick as the olympics r comin!) it's very good