If you all are adamant on SWA (I am to, so don't get me wrong), you may want to look at Ding! for your fares. You'll generally get them cheaper through their app than what they post on their sites on Tuesday and Thursday. Again, you'll have to jump on them fast, because the Ding! offers end at certain times.
Right now, here's where you'll want to fly into if you want alternates to Reno, in order of distance (closest to farthest from Reno):
SMF (Sacramento)
SCK (Stockton - be aware, this would be Allegiant, and they don't fly everywhere)
OAK (Oakland)
SFO (San Francisco)
SJC (San Jose)
FAT (Fresno - This may be a puddlehopper, so may be more expensive)
If you are looking for the 7 - 8 hour drive, instead of Vegas, and dealing with the 2-lane drive all the way up, consider SLC (Salt Lake City). It's roughly 8 hours east, and all on I-80.
But I'd definitely say that SMF is your best bet for an alternate. I also recommend it because.. well, I live in Sacramento!