Hello there Sleepless. I haven't spoken to you before here on JREF, so I guess I should say.. Welcome to JREF!!
To answer your question:
へ is used to denote a general direction.
に is used to point to a specific place.
For example:
東京へ出発する
とうきょうへしゅっぱつする
Toukyou e syuppatu suru
To leave for Tokyo
東京に着いた
とうきょうについた
Toukyou ni tuita
I arrived in Tokyo
Hm.. Maybe it's not such a good example but I couldn't think of a better one. I guess it's a difference in nuance. You're right in observing that に can also be used for time ("I left at three"). It can also be used for things like denoting who you spoke to ("I said to Mr. A") etc. But that's a whole different subject and I don't know if you want to elaborate on that.
If you want to say "I want to go from A to B", I'd say:
AからBへ行きたいです
AからBへいきたいです
A kara B e ikitai desu
から and まで could be in sentences like:
AからBまで列が並んでた
AからBまでれつがならんでた
A kara B made retu ga narandeta
There was queue from A to B
So basically that means more like "from A to B" in sense that it expresses the limitations or borders. (God I'm bad at explaining this!!)
And again, it can also be used in time-related subjects:
1から3まで働いた
1から3まではたらいだ
1 kara 3 made hataraita
I worked from 1 to 3
Hm. I hope my explaining hasn't made matters worse for you!