I'd say your three choices are SYR, HPN and BDL. One of the great things is you may change your base every 30 days, so you can try a few of them a decide what works the best. Each of those choices have some different benefits depending on what is important to you. If you do not like riding on airlines I'd recommend HPN, you will probably airline less and majority of the time you will get a limo to TEB or have a plane in HPN. Also you will have free parking in HPN for sure. BDL is the closest. SYR could be something to play with for three reasons, first I believe if you are going for the after-midnights ($960.94 1st year), you will get more being SYR based then any of the others (I know people who drive from RDU to FAY for this reason). Second, you will most likely airline on your first and last day a majority of the time building lots of miles and status. Not having Southwest is an advantage if you are interested in that. Third reason being tickets in and out of SYR tend to be on the high side, being a good advantage if you prefer to use dummy tickets. Remember YMMV but you will want to try each of them and see what works best for you.

You will have a hard show time for your first day by 6pm the evening before. You get home on your last day when you get home, if it's after 12:01 (parked at gate on airline) you get the $. No consideration is given for your drive time to your house.