definitely consider Menlo Park along with Redwood City.
as far as finding a place to rent--it's rather difficult to do that here when you aren't physically present. Things get gobbled up fast, and the typical practice is to have a security deposit and ability to sign lease all ready to go when you view it.
Landlords will open the place, schedule several people at once, and basically award whoever has everything to go--they will do the credit checks and all that, but if you aren't ready to hand them something when they first meet you, then you are likely out of the running. On top of that, you really do want to see the neighborhoods. The photos on CL or apart finder will hide everything you actually want to see. There are good and bad neighborhoods most everywhere around here. Though, even some good neighborhoods "look bad." (me, coming from NC and Chicago...the typical neighborhoods just look different out here)
and yeah, getting to Redwood City from SF isn't that great. well, you can just do Caltrain, but that involves transit from the Caltrain station in Redwood City.
Oh, also consider San Carlos or San Mateo--both just north of Redwood City.
Why San Carlos?
http://refugesc.com/
you're welcome.
as far as the middle of Redwood City and Fremont...that's basically San Jose, Los Gatos (I think?) that area, just on the south end of the Bay. Fremont and Redwood are basically separated by the Bay, though you have two bridges on either side of Redwood. PT, if that is your plan, wouldn't be easy (BART ends at Milbrae on the West Bay--about ~10 miles north or Redwood; and at Fremont on the East Bay....don't even dream of using BART/Caltrain to get from Fremont to Redwood. Just...just look at the map

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