Ex. 1 is an interesting groove I played on “Go-Go,” the opening track of Galactic’s first record, Coolin’ Off. It’s a fun linear pattern that can help develop coordination as well. I originally played this with the right hand on a muted snare with the snares off, set up to the right of the floor tom. Live, I usually play it on the cowbell. On Ex. 2, note that the right hand cowbell rhythm is the same as the accents in the standard street beat. Ex. 3 gives you some variations you can use as fills or other grooves.
You can try putting the right hand on the small tom, hi-hat, ride cymbal, floor tom, timbales, etc. As usual, try playing these in between straight and swing. Have fun with these and try to come up with your own variations.