While I am in Fiordland, I wanted to take a cruise. I am looking to do a cruise that would be a few hours (vs. overnight) and not cost more than NZ$75 per person since I'm on a tight budget. Is it possible to visit Doubtful Sound on this type of time/cost budget?

Any recommendations?

We enjoyed the Nature Cruise on the Milford Wanderer, which costs NZ$80 each for a two and a half hour cruise. It's a lovely boat with sails and more character than some of the boats, it's also used for the overnight cruises.

http://www.realjourneys.co.nz/Main/DaytimeCruises/

Just re-read your post and saw you mentioned Doubtful Sound. The reason these cruises are more expensive is that to get to it, you must first get a boat across Lake Manapouri, then a coach over the gravel road built for the power station - that's about a 90 minute trip (each way) before you get to the Sound itself. If you drive to Milford Sound there are all sorts of short cruises available.

redpen: Your subject says Milford Cruise, but in the body of your post, you talk Doubtful. Which is it?
For your budget, as Maria H explained, forget Doubtful.
Driving to Milford though works. Check out the many boats and tours available, should be right about your budget. Just google Milford Sound, you'll find about 4 companies. It's beautiful, and the drive is awesome also.

Milford Sound is lovely and the drive out there from Te Anau is fabulous. If you have your own car, then doing the drive yourself will save some of the cost. But make sure you give yourself enough time. We decided to just drive staright through without stopping in the morning and then did our stops on the way back. We did the Milford Sound Cruise with Red Boats and enjoyed it a lot. I can't remember the exact price, but they were all pretty much the same. We elected not to have the buffet lunch and just requested a sack lunch which was fine. You could also bring your own food. We really wanted to be up on deck most of the time anyway (even when it was drizzling) and not be inside eating. I can do that anywhere!

We did Milford this past August and it was fantastic. We were in Queenstown and our next stop was Milford. It was suggested to us that we self-drive to Te Anau, stay overnight and then hope the Real Journeys bus to Milford for the cruise. We were told that the sights and views during the drive between Te Anau and Milford are so incredible that you don't want to miss anything while self-driving and having to pay attention to the road. I think this was one of the best suggestions we got during our whole 3-week trip. Taking the bus was the perfect choice, and really not too expensive at all. Once we got there, we boarded a Real Journeys boat and the tour around the sound was breath taking.