I absolutely agree with the other comments about going for binoculars over a cheap scope. Go for binoculars with big objective lenses and don't go for huge magnification. While you want some magnification, what you really want is to get more light into your eyes. With binoculars like that, you should be able to see lots of interesting and beautiful things in the sky. You may be able to find an old pair in a second hand shop... Goodwill for instance?

As for telescopes, you won't find anything that won't frustrate you terribly for the kind of money you're talking about. I got a department store scope when I was a kid, and it just drove me nuts. You might look into making one. One of the popular telescope designs is called a "Dobsonian". It's a simple telescope, often made from cardboard tube and plywood, with a home-ground mirror. They are named after the guy who developed the design, John Dobson. He used to make these telescopes and take them out in San Francisco and show the sky to local kids. Sometimes, he'd give one away to an eager kid. He was a monk (if I remember right) and had to make them cheap.

Look around your area and see if there is an amateur astronomers' club around. If so, there are bound to be old codgers there who would be helpful with advise on getting into astronomy, what sort of equipment might be good, and how to make your own, if that sounds interesting.

Don't forget, by the way, that you don't have to have expensive equipment to get into star gazing. You just need at least one eye and clear skies. Although having a star chart with you (either printed or an app) would be a big help too. Binoculars and telescopes will show you more, but there is a lot to see just by looking up.