Henj, thank you so much for your advice! An assistant position with a solo-practice lawyer would be perfect for me, I'm definitely not counting on any big firm stuff. Could you tell me more about how you were able to find that job? A job at the government in Washington DC is a possibility. I would have to move all the way to East coast, which is not that convenient, but still a possibility, I guess. I should look into that too. Thank's for the advice!
I actually live right now in the city of Seattle, Washington State (that's Pacific Northwest, not Washington D.C.). It's a medium/largish size city, so there's plenty of firms and private legal practices. I should be able to find something. All the ideas about how to look for an internship are very helpful!
I had a similar situation and had to wait a year to reapply. I had low LSATs and didnt apply to any real safety schools. I went a bit extreme and moved from Texas to DC and found obtained an internship at an NGO. While interning in the first three months, I retook the LSAT and increased my score. I also found a job at a large law firm and became a conflicts/new business assistant.
I found the job on a whim: looked to www.vault.com
and sent a letter and resume to every law firm that had a DC office. I only received one phone call out of the 75 letters I sent and got the job the next day. I worked at the internship and the law firm at the same time, so I was definitely busy.
This was all well worth it because when I reapplied, I was accepted at two law schools that rejected me the year before and my current law school actually highlighted my work in the law firm and internship in my acceptance letter. Even though I increased my LSAT score, I only had a 10-20% chance of getting accepted per Chiasu.
A lot is based on luck, so definitely apply to as many law firms as you can. I initially applied as a "paralegal," but the firm only needed a conflicts assistant. I didn't do much "legal" stuff, but I gained exposure to a large law firm and I made many contacts. Good luck.