That depends on a couple of things.
1. How much yeast are you adding to your starter? If you're starting with a smack pak full, then overnight is fine. If you're starting with some frozen yeast, you'll need a few days to get it really going. Same if the smack pack or refrigerated yeast is old.
2. Are you using a stir plate? If you're allowing air exchange either through a foil cap or foam plug, the spent beer will be oxidized and won't be a good thing to add to your wort. Make the starter up a day or so early and then the night before, crash the yeast out in the fridge. Decant the spent liquid and resuspend the yeast in some chilled wort before pitching.
3. If you need a lot of growth, keep the starter upstairs. Yeast will grow faster in warmer areas, much warmer than you'd normally ferment (you're making yeast not beer so don't worry about fusels and off flavours in the starter, esp if you're crashing out). 80F is close to an ideal temp for growth, yeast can tolerate up to 90ish.
But... if you're starting with a lot of healthy yeast and just need more, using an airlock and plan to pitch the whole starter, then yes, set it up in the basement