I hate to post a differing opinion, but you can absolutely upgrade the speakers and have better sound with the stock HU.
Do your ears hear the head unit or the speakers?
The head units in factory vehicles are usually of pretty high quality. I recall Honda stock units being made by Alpine about 20 years ago, but I have no idea if they still are.
I have seen factory HU's place in stereo competitions after having added amps and speakers to them. The main thing they need are better speakers, more power, and a way to equalize the sound.
The factory stuff isn't that bad, it just lacks the bells and whistles the aftermarket stuff has. However, if you simply change speakers, you may not be all that impressed until you also add an amp. More power will almost always make the sound better because it gives you more dynamic headroom, as in it gives you more useable volume before the head unit starts clipping.
In my wife's last T4R I added an amp and a woofer to the stock system and it actually sounded pretty good. It really exceeded my expectations. I'm usually not a fan of line level converters, but it sounded really clean. I'm going to reinstall the woofer in the new one when I get a chance. Really all the stock system needs for her listening tastes is more bottom end.
In a nutshell, it's best to upgrade everything at once if you can, but you certainly can replace pieces and parts as you see fit. If you are not adding an external amp, you won't see a huge increase in sound by changing the speakers unless you go with really good speakers (Infinity, Alpine, BA or the like...), as I said before, the stock stuff isn't all that bad. Changing the HU to an aftermarket high power unit will give you better sound quality out of the stock speakers, but it will also increase the likelyhood of them blowing after a while.
Personally, I really wouldn't have a preference between adding an amp and speakers to the stock HU or changing the stock HU and changing the speakers too. Best would be new HU, amp, and speakers of course...
If I was going to only do one thing, I'd add an amp and woofer to the stock system as my first choice. Second choice would be a nice set of Boston Acoustics speaker replacements and leave everything else stock. An additional amp to choice #2 will make a big difference.
I personally wouldn't do a HU change unless it was to a very nice HU with a ton of features. I definitely would NOT change to a Walmart $150 Pioneer. There are a few nice ones that I would consider, but they all seem to cost upwards of $500. That isn't going to happen for quite some time.
Sorry this post has seemed to ramble on, I was typing as I thought which is rarely a good thing.
I may not have given you the answers you were looking for, but discussion is always good. And discuss the issue, I have definitely done.
