Worth buying cheap bike for NYC?

I just started a year off work and love using the citibikes here in NYC for the past 10 years. I would love to start taking longer trips to explore the city now that I am not working. But the second day after I moved to NYC 20 years ago, I locked my $400 trek bike with a gorilla U lock to go into a store for 3 minutes and when I returned the bike was stolen. I used that bike for 3 years in Boston without problems.

Is a lighter bike then citibike that I can use for more that 30 minutes worth it in NYC?

Thank you!