You are overdue (based on time) for a timing belt replacement.

The water pump & timing belt tensioner are usually replaced along with the belt. This is because if either part fails mechanically, it can lead to the belt either jumping a tooth or failing altogether.

And since the motor in your Integra is an interference design, you do not want to risk having the timing belt snap.

Ask your mechanic to quote you only for the timing belt, tensioner & water pump replacement only. That should knock the price down substantially.

I'm not one to skimp on preventative maintenance, but I'm skeptical about what hoses your mechanic feels ought to be replaced at this point.