Volunteering opportunities in Tel Aviv?

There be a lot of places you can volunteer if you contact places directly. The problem is that many of them require you to speak Hebrew. There is one place I know of off the top of my head that don't require a lot of Hebrew: the African Resource Development Center (http://www.ardc-israel.org/en/volunteer). You may also be able to do something with Doctors Without Borders or the UNHRC in Israel, who work primarily with non-Hebrew-speaking populations.

You may be able to find something at the universities as well, since much of the research there is done in English and the academic lingua franca is English. Depends on your background, though.

If you and your boyfriend have been together for a significant amount of time, you may be able to get a partner visa which would allow you to work; however, if you don't speak Hebrew than your job possibilities are going to be limited as well. If you don't qualify for a partner visa, a 6-month volunteer visa is relatively easy to get provided you have a letter from an Israeli organization saying that you're volunteering there for six months.

Thank you for your reply!
I now have more options to look into!
May I ask what you mean when you say there may be something at the universities? Do they sometimes want volunteers to help with research?
The partner visa is something which I considered but wasn't sure was open to me. He and I have been together for 4 years, but as he is in the army I will not technically be living 'with' him, even though I'll be staying predominantly at his family home. I fear that because we won't be living together for the majority of the time I will not be eligible for a partner visa - I don't know if you have any further knowledge of this, or know where I could find out more? Being able to work would be ideal (even a small job!) but I didn't think it would be possible to obtain a visa!
Thank you so much once again, contacting volunteer places directly seems to be the way to go and now I have places to start! So thanks!

Many of the universities do research, so you may be able to volunteer/work helping professors with their research: writing things up, analyzing statistics, helping with literature reviews (since most scientific journals are in English), stuff like that. You can also check out some of the listings on the internship program sites, and then contact them directly (for example http://www.regcareerisrael.com//InternshipSearch.asp). Google what interests you, find people in Tel Aviv that do that stuff, and send them an e-mail that says you're willing to volunteer. I'd think many places would be keen on free labor.

As for the partner visa and not living together: I don't know. It's worth your boyfriend calling the Misrad Hapnim and asking. They required us to show a lease with both our names on it when we applied; maybe they'll waive that since your boyfriend's an active duty soldier, especially if you have four years worth of evidence of the relationship (photos, e-mails, etc.). I don't know, but it's worth checking into.

I hadn't thought about volunteering as an intern, that's a great idea! I wonder if that will still be able to count on a volunteer visa. I'll need to see if I can find out.
Also I'm in Israel for a holiday in October, so perhaps I'll be able to see what opportunies there are in person, now that I know there are possibilities - just ned to find them!
And you're right, the partner visa is worth looking into because if it is possible that would be amazing! Definitely worth getting him to ring the Misrad Hapnim.
Thank you so much once again!