Search the USPTO TESS database (free), then search Untappd and BeerAdvocate for active breweries with similar names. Existing trademarks in beer category 32 are absolute blockers.
Should my brewery name include 'brewing', 'brewery', or 'beer'?
'Brewing' or 'Brewery' is standard and helps SEO and customer recognition. 'Beer' alone reads amateur. You can drop the suffix entirely if the name is strong on its own (Stone, Sierra Nevada).
Can I name my brewery after a place?
Yes, common and works locally. Check the place isn't trademarked (some town names are) and consider if you ever want to ship out of state — local names hurt regional brand pull.
Are punny brewery names a bad idea?
Puns work for taprooms (entertainment), poorly for cans on a shelf where you compete with serious craft brands. Pick puns only if you're bar-first, distribution-second.