I might be safer than you think. I used to refuse to ride in a city because it seemed dangerous and many people I knew who rode in traffic had been in accidents with cars. But when I ended up on a bike trying it out, I found I could almost always (~95% of the time) avoid traffic, even without bike lanes.
Side streets and alleys are great - too slow for cars, but you're probably cycling at 10-15 mph, which is fine. Parks can be great - a shortcut with no cars and beautiful scenery, while the cars have to go the long way. Campuses, plazas, etc. etc. Even sidewalks when empty or nearly-empty can work to bypass traffic or go the 'wrong' way.[0]
[0] Second to riding, cyclists love to lecture others on how to ride. And a favorite outlet for their obsession is sidewalks. They don't discuss or consider the reasons or merits, they just have found an easy outlet for self-righteousness and repeat the same phrases over and over. Just remember that sidewalks are for pedestrians first; you are a visitor. Give them the right of way always, let them know when you're behind them (e.g., 'on your left!'), and give them plenty of space (trying walking when a bike buzzes past in either direction - from behind, you can't even hear it coming). Defer to their safety, real and perceived. It's easy. No problems at all IME, except self-righteous people over-excited at an opportunity to lecture someone.
If you're particularly envious you may want to consider asking how those who can't drive make do in your location. Life's about making choices and seeking different perspectives might help change and/or inform your priors.
