My options:
1) stay 8 hours at LGA airport (not my 1st choice)
2) get hotel room near LGA
3) explore downtown (problem: 2 large bags)
Aside from getting a hotel room near LGA, there is no baggage storage at or around LGA.
Also- the poster who commented on the "4 hour" rule for airline check-in is entirely accurate...often times your reservation will not even show up on the self-service kiosk until 4 hours beforehand.
If you don't mind schlepping to Manhattan with your bags (most likely via cab), Schwartz Travel (36th St. b/t 8th and 9th Ave) will store your bags for a few hours. You are then free to explore. Fees are $6-$10, and they stay open pretty late at night, so you don't have to worry about them locking up with your luggage still inside.
Lastly, if you are trying to get to Manhattan on the cheap and don't want to pay the $45 straight cabfare from LGA, I believe LGA Airporter makes the run in their coach buses for $12.75 one way. They drop at the Port Authority at 42nd- from there it's a short (and much cheaper) cab ride to Schwartz.
Link to Schwartz is below:
http://www.nyc.com/visitor_guide/lug...al_review.aspx