I have a '97 Accord with 94k miles on it. Recently I've heard dull but loud
vibrations coming from underneath the car as I'm accellerating, especially
uphill. I sometimes hear the same noise a few seconds after I start the car. Also the accellerations in general have been getting louder. Any
ideas as to what it is?

On another note, should I go to the honda dealers or any reputable auto
shop (Auto Zone, etc) for repairs and maintenance

 

Check your exhaust system (from the cat to the muffler). If this is rusted through or rusting through it will sound like a "performance" exhaust but will definitely kill any backpressure you want/need. As far as the maintenence, get a manual, a few tools, buy the parts at Autozone, and do it yourself

 

if you know nothing about your car
go to the dealership.