Regarding dialects. I wouldn't be concerned about the difference between the central dialect and the northern. I haven't had any problems being understood speaking Thai, in basically any context and situation for the last 20 years. I live in Chiang Mai and I speak central Thai. I don't use specific words in the northern dialect, but when I go to other places in Thailand some people there, sometimes points out that I sound "northern" even though I can't hear it myself.
Thai people up here easily switch between northern specific vocabulary and central Thai vocabulary. In Chiang Mai, if you live among Thai people you will inevitable be exposed to both. As you know, there are a lot of foreigners who never learn Thai because everyone speaks English with them. The same rule applies if you speak central Thai up here in the north. After 20 years of speaking Thai everyday, I still can't understand more than very parts of the northern dialect. If someone tries to speak real hardcore northern dialect with me... I am totally lost.
I would definitely prefer to learn Thai in Chiang Mai compared to Bangkok. I think the culture in Chiang Mai being easier to integrate with. But, I am just guessing since I have never lived anywhere else. A definite recommendation from me is to stay away from places where you are likely to be considered a tourist among Thai people. Here in Chiang Mai, if I go into a 7/11 or go to a restaurant it is much more likely that they initiate a talk using Thai than English. I don't think that is the case in many other places, instead they simply either avoid you or try to address you speaking English.