Since the dumbbell bench is the best exercise for chest development, I’m guessing that’s what you’re going for. You can use the chest press, incline chest press, cable press, pec deck, and dumbbell or cable flyes. Dips can be used if you lean slightly forward, otherwise you’re targeting your triceps. If triceps development is your main goal, you can do tricep pushdowns, overhead tricep extensions or lying tricep extensions.
If you don’t really have weights available, you can always use the good old fashioned push-up. Try different variations such as the diamond push-up, uneven (one arm supporting on something higher than the floor), arms placed far appart etc.
Don’t forget your back though. Exercises such as the barbell, dumbbell and cable rows, as well as the lat pull-down, pull-up and chin-up.