Hello - welcome!
My husband and I also bought two 2003 Accords at once - ours are both 5 speed DXs. They both run very smoothly with no vibrations ever, A/C on or off.
However, there has been a lot of discussion here about various vibrations in the 2003 Accords. I think that it's mostly the more expensive models - EX and both V6s - that seem to have the problems, for some reason. Hopefully some of those people will respond to you here - but, in the meantime, you can access all those threads by doing a search. Good luck!