1. Weighted DipsThere is absolutely nothing wrong with using bodyweight exercises like the dip. The point I want to make by distinguishing weighted vs unweighted exercises is that it's always easier to transfer progress down than it is to transfer up. Another words, if I can increase my unweighted dip max from 20 to 25, I may see little to no increase in total strength. If I increase the amount of weight I can handle with 95lbs+BW for triples to 100lbs+BW for triples, you can bet your ass I have gotten bigger, stronger, and will likely be able to do more unweighted dips as well.
If I hit all reps, increase max by 2.5-5lbs
2. Weighted ChinsSee the argument for weighted dips. As another quick example, I went 5 months without training bodyweight chins. At the end of a long workout, I hit 19 chinups without trying. Do weighted chinups.
3. Glute Ham RaisesThese are hard as shit, and will make you walk funny for days. I use them because I have trouble activating my hamstrings and glutes with squats and deadlifts. As an assistance exercise, there are no better bodyweight exercises.
If your gym does not have a glute ham machine (very very likely it does not), lock your legs down wherever you can and slowly descend towards the ground. Keep your back straight, and let your hamstrings/glutes resist the descent. To assist the return, it is likely you will need to push off the ground with your hands.
The goal is to hold weight in your hands, but it will be a long time before you will be able to do so.
4. High PullsLike a powerclean without the clean. Deadlift the weight up, then pull the barbell up as high as you can. The last motion will be a violent pull with your traps which should leave you sore for days. The benefit to this exercise is that you can pull far more than you can clean.