If you decide to go the healthcare tech route, Haas is probably better for that than Kellogg. You would be able to visit the start-ups at any point and could do local coffee chats with all of them by taking the BART for 30 minutes. It's definitely possible from Kellogg, but you would likely have to do semi-frequent treks to San Francisco and there will likely be more leg work on your end (you could also probably do calls via the phone, but you are not going to get as good a feel for company culture). This is obviously contingent on wanting to stay in the Bay Area as Kellogg would have more pull in other parts of the country. If you go to the alumni pages of each on LinkedIn (Type Kellogg School of Management and then click Alumni tab) and then type in companies that you may be interested in joining, you can get a feel for how many alumni from each school are at each company. This will be pretty important as they will be the ones you will be doing initial outreaches to when recruiting.
Re: alumni base in SF, from full-time programs, they are probably placing similar amount of students in SF post-graduation, but the key difference is that Haas also has the exec / part-time programs whose graduates are pretty much all staying in SF (another 350 / yr with 50%+ coming from the tech industry). Berkeley as a whole also obviously has a massive alumni base in the Bay Area, particularly in tech.
With all that being said, from what I have heard, pretty much everyone who wants consulting gets it from top schools, although many will go to other consulting firms than MBB.