Where can you pick up basic Hebrew?
You can start by checking out free lists of common Hebrew phrases such as this one. While not the easiest to learn from, they should help you with the basics and may be enough for a short visit.
People in Israel, particularly Tel Aviv, speak decent English. Almost anyone you meet will be able to give you directions. Most can have actual conversations with you and are more than happy to practice their English at any given opportunity. This means that learning Hebrew is not really necessary if you are just visiting and all you want to do is get by.
Learning how to say shalom (“hello”, or “peace”), Toddah (“thank you”), ken (“yes”), lo (“no”, pronounced like the “lo” in “lock”), and “kamma ze” (“how much is this?”, the “ze” is pronounced like the “ze” in “zed”) should be enough to endear you to locals, and they will undoubtedly be keen to teach you some local slang, too.
If, however, you’re visiting for longer or moving to Israel (or are just interested in picking up the language), the locals’ enthusiasm for speaking English can make it more difficult to casually learn.
Hebrew is considered a difficult language to pick up, and Israelis are notoriously impatient. Most will switch to English if they’re talking to someone who’s visibly struggling with the language.
You’ve probably heard about the “Ulpan” – the intensive method of teaching Hebrew used for teaching olim (Jewish immigrants to Israel), often for free. If you need to pay for it, it’s usually not cheap, plus, being an officially sanctioned Israeli method, some people find it’s not in keeping with their own politics (basically, if you’re a lefty, or at all alternative-looking you’re going to have to just smile and ignore a lot of stuff taught as gospel, as well as possibly be picked on by teachers). Of course, if you don’t live in Israel, finding an Ulpan is not going to be as easy anyway. See below for alternative options.

Where can you learn Hebrew in Tel Aviv?
Normal Ulpans involve a lot of very thinly disguised indoctrination. If you’re a die-hard Zionist, that might suit you just fine, in which case you can find plenty of those on Google. If you’re Jewish and making Aliya, I believe you get to go for free. Otherwise, you may find yourself struggling with the dogma (and the costs).
Tel Aviv’s grassroots Hebrew school, This is not an Ulpan is a good alternative. It’s a socially conscious Hebrew school, where learning is done using Hebrew, while you actually learn about various aspects of Israeli culture. They offer small group sizes and really unique classes and courses.
Ulpan Bayit, is another good alternative, with friendly teachers and small group sizes.
Where can you learn Hebrew outside of Israel?
Online classes
Both Tel Aviv-based Hebrew schools above now also offer online classes, so you can join a group from the comfort of your own home (time difference permitting).
Independent Learning (Online / App)
Alternatively, you can also do online Hebrew courses using a website or an app.
My favourite is Hebrewpod101.com which a site I’ve partnered with after I used the same app to learn Japanese before a trip to Japan (spoiler: I picked up enough in two weeks to be able to order food, ask for directions and other needful things!).
Their marketing is aggressive, but their system works really well. There are actually enough free classes on there to get you started, but if you want to sign up for the paid membership options, you can save 25% by using DIYTELAVIV as your discount code. Obviously, I get a small commission when people sign up, but I wouldn’t have partnered with them if it hadn’t been for my great experience using their services myself.
Duolingo is another app that offers free Hebrew lessons. Their teaching method involves short lessons you can do in your free time. No official grammar instruction (not much, anyway), but you learn by repetition, sort of like the way kids learn. I’ve been using it to learn German, Yiddish, and Spanish and their system definitely works.
Language Exchanges
If you’re abroad or want something more flexible, there are a few things you can do. You could join an online language exchange (like mylanguageexchange.com) and get a Hebrew speaking pen-pal who wants to improve their English (or another language). I’ve actually made some good friends like that and it has helped me with my Spanish, but it’s best if you have some basic experience with Hebrew, as these are not professional teachers. There are actually some language exchange sites where it’s actually a paid service with Israeli teachers giving online private lessons. A Google search brings up literally hundreds.
By the way, there are a few language exchange groups in Tel Aviv too, and other parts of Israel. Just search for <city> language exchange on Facebook and you’ll find them. I sometimes list them on my Tel Aviv event listings page.
Streetwise Hebrew Podcast
Guy Sharett, the awesome polyglot who runs the Streetwise Hebrew Podcast, used to also run some Amazing tours of Tel Aviv that taught you Hebrew, but sadly, he no longer does. However, you can still enjoy his bitesize podcast and learn colloquial Hebrew.