Wow 4 weeks in San Mateo that's a long time. We are across the Bay from San Mateo so I'm not really familiar with any running groups. Since it's the Bay Area...(and if you have a car) you can drive about 20-30 pretty much any direction and get to some other locations where there are more options for you.
Foster City is one town over with water canals running through it and walking/running trails around a "lake" area. Palo Alto, Stanford, is about 20 min South from you and the entire town is biking and great places to run around campus. In San Mateo a couple of places to try Crystal Springs Reservoir:
http://www.traillink.com/trail/crystal-springs-reservoir-trail.aspx always crowded on weekends with runners, bikers, walkers.
San Mateo Running Routes:
http://www.walkjogrun.net/running-routes/USA/CA/San Mateo/
Yelp has some other suggestions along with a map. Yelp San Mateo Running Routes:
http://www.yelp.com/search?find_desc=Running+Trail&find_loc=San+Mateo,+CA
Hillsdale Mall is in San Mateo --Nordstroms and Macys as well as Cheese Cake Factory. Which now has an extensive healthy menu options.
The weather----it's generally foggy in the a.m. and p.m. and clearing up in mid-day. But it's not uncommon to have rain showers in June or even a heat wave. So I'm not much help with that. I guess pack a little bit of everything.
Hope this helps and gets you started. I'll keep thinking of more ideas.