College is a great place to check if you are looking for a place to make beats. Community colleges and universities often offer classes in music composition or the recording arts, and many of them have facilities that will allow you to make your own beats. Sometimes, students have access to the computers with beat-making software without having to take the class. However, some beat-making software can be complicated, and if the class is inexpensive, enroll in the course to learn about the software with a qualified instructor. As an added bonus, many music-making software companies, such as the makers of Pro Tools, offer considerable student discounts on their software.
With an investment of about $200, you can buy a used drum machine and a 4-track tape recorder and start making your own beats. The next step up from there is to buy a capable computer with sufficient memory to run the latest version of Propellerhead Reason, plus some good monitor speakers. If you are really serious about making beats, you should invest in a copy of the industry standard: Pro Tools. To use Pro Tools, you need a dongle or a Pro Tools compatible recording console, so don't just buy the software. To make sure you get an authentic and functioning version of Pro Tools, buy it from an official dealer.
Another great place to make beats is at a friend's house. If your friend happens to have recording equipment or beat-making equipment, then you can use her equipment for free instead of buying your own. If you don't have recording equipments, you can always beat-box or use household items for drums, and record it with whatever equipment is around the house.
If you want to make beats live with some friends, try a drum circle. A drum circle is a meeting of people who want to beat on a drum simultaneously. Generally, you can beat on what ever type of drum you'd like. Sometimes you can get away with having only a pair of sticks or a spoon and a bucket to drum with. Some drum circles even have drum rentals if you show up without a drum. You can start your own drum circle if there are no regular drum circles in your area. See Resources for more on drum circles.
If you don't have anything available to record beats with, you can always come up with new beats to use when you do have a recorder. If you have a tape recorder around the house, you can beat-box the beats you make up in your head while you are out. Most computers have a sound card and a microphone plug in, and include some kind of simple sound recording program, usually in the Accessories panel. You can use this basic setup to start making your own beats.