akpak, congrats on graduating, that's a wonderful accomplishment!
For commutable towns to Manchester, you might want to consider Manchester (watch the neighborhoods tho...), Hooksett, Goffstown, Londonderry and depending on what side of Manchester you're on, Merrimack. You could also consider Salem (south of Manchester on I93) since you'd be going in the opposite direction of the majority of traffic.
One area to check out in Manchester is Eastern Ave, just off Wellington Road (Exit 8/I93). There is building after building after building--don't know if you'd consider something like that but check within the lease office for more details.
I send you a direct message with some apartment listings under $1000 a month, maybe something there would work for you. Anyway, best of luck