There are a lot of exercises to improve your balance. Basically anything where you have to concentrate on your balance, as keeping your balance needs in first place that you recognise when your body leaves an optimal balanced position of the stance in which you currently are. That sounds logical, but people are not aware of that.
So there basic exercises which you can do at home (or anytime anywhere if you don't feel embarassed) without buying any extra stuff.
- First of all, pay attention to not being flat footed. Have the majority of your weight (70-80%) on the balls of your feet. In the beginning you could lift your heels completely, so you really get used to having your weight on the balls of your feet.
- Walk slowly around, and I mean REALLY slowly and be conscious not only of every single step you do, but try to be conscious of every fraction of the movement of your step. Stop your steps mid-air and try to feel where your center of gravity is.
- While walking slowly do "silly" movements (search for "Silly Walk" in youtube, but do the motions much slower) and also do level changes. It sounds and looks silly, but it brings you body in unusual positions so you have to pay extra attention on your balance.
What's important is that you spend a lot of the time of your motions on one leg, because by that it's much easier to learn how to recognise when you leave your optimal balanced position (on two legs you may have left your optimal balanced position, but still can stand, so you don't get the feeling)
That's for your conscious balance training. To that you can add "half conscious" training.
- I.e. standing on one leg while brushing your teeth, cooking or what ever you to standing. That way you have to split up your concentration on your balance and on the task you're actually doing. That helps to develop a better unconscious awareness for your balance.
That's stuff you can do without spending a single penny. But if you want more, you can of course spend some money to support your training and make it even more effective. For example you could buy a balance disc, balance board or other equipment for balance training.
Then there are other activities that would support your balance training. I.e. skateboarding or surfing like Budhisten said. Others would be slacklining, parkours or gymnastics. What's also great is dancing, in particular Tango, ballet or contemporary dance as they work a lot with the axis of your body and balance.
Finally a special advice for your BJJ training: At every training session use one sparring round particulary for your balance awareness. That means don't try to throw your opponent in that round, but focus only on feeling your balance when he is trying to throw you.