Warmer Weather is Here... Secondary Temps?

I will get right to the point:

For an extract-ale brewer, what is the ideal temperature to age at after fermentation winds down (regardless of if its in the primary or secondary)?

A range is fine... I know each beer is different, but I have come to see that most ales do best when primary fermentation is in the 65-69 range. Of course some a little higher and some lower...

It is looking like I am going to have a closet ~71-75F and a basement ~63F-66F

Im not a professional so take my advise with a grain of salt if you'd like, but I dont believe temp control is AS important in secondary. Yes, there might still be a little bit of active yeast but it wont be actively fermenting so not as big a deal. I keep mine at room temp while in secondary. 70-72 deg.

IMO you wan to keep it under 80F. My house can get that hot in the summer and I've not had problems with it. The beer will just age faster.

Is it ok to allow a belgian double or triple to age for a month or 2 in the mid 60s?

Mid sixties are perfect for aging. If you plan to cellar it you want it closer to 55.