I lack the contacts for finding a better job in my local area. Does anyone have any tips for finding a better job in the short term without spending months making new contacts? I'm tied to my location for another 10 months due to renting.
You'll need contacts to some extent (or at least they'll help a lot). Go to a local developer meetup and meet people/hand out business cards. Always have an example of your work with you to show to people.
If you're really desperate, you could try sites like oDesk or similar.
It depends on what sort of job you are looking for and at what type of company.
I suggest building a proposal of what you would do to improve X at Company A. Say, for example, you're interested in [role] at target companies A, B, and C. Providing them with 'free', outsider consulting is a good way to a) validate your expertise, b) show that you're interested in the company and c) start a conversation out of the blue, and perhaps make a few contacts quickly.
Try to back your way into an understanding of their strategy and tactics for X through a lot of observation and research (shouldn't actually take that long). Then, do the same for their competition, or find analogous examples in another industry. After you have a feel for their strengths and weaknesses, you could identify the gap between what their competitors do really well and what Company A does not. Then, make a thoughtful, quantitative approach for how you would improve the company's standing in X, or redesign page Y to increase R based on what you know about T. There are a lot of ways you could take this.
Summary: demonstrate your understanding of the company, the problem you want to help them solve, and your solution. Send it a person in the respective department or even Tweet a link to your proposal at the company. Best case scenario: they hire you. Worst case scenario: they don't, but other companies take notice and you're building a portfolio.
Are you sure there isn't some flexibility in your renting? Some landlords just want to make sure their place doesn't sit vacant, and that they don't end up with a series of short-term renters.
If your lease is the only thing holding you there, you might ask your landlord if you can leave early. It can depend on the landlord, and the local real estate market. Recruiting someone to take over the apartment can make the idea more amenable to a landlord as well.
I have my GitHub profile, but it doesn't have much on it except a few random open sourced projects and some random open source contributions. A lot of other work is for past/current employers which I can't exactly show off easily.
If you're really desperate, you could try sites like oDesk or similar.