travel and rhum

I’m currently in California on a military training exercise and from the UK. We have 5-6 days at the end (beginning of November I believe) to basically go off and do as we please and I’m in a bit of a rough spot financially due to a house purchase so whereas everyone I know is looking to go to LV/LA I’m a bit more inclined to go somewhere and spend a bit of time on my own just doing some running/hiking but I haven’t a clue where to go. I’ll probably end up getting a flight somewhere, ideally a base location with good food/transport links with some good mountain trails. Just looking for some general recommendations of where to go/what to do that’s not gonna break the bank.
Many thanks!