Now, I quit going to games a few years ago and part of that was indeed expense but ...
Day games during the week ... period! against any other team but Boston and you can get in.
You can still get upper deck or bleacher seats for under $20
There is a great diner around the corner that is real cheap. I just go early to the game and have a late but huge breakfast and only get a water or soda at stadium prices.
Scalpers for good seats ... You have to be careful and yes I got burned in a "sleight of hand trick" once .... but .... once you get to know a scalper (they will give you their phone #), you can also get decent seats cheap during the week since if a scalper doesn't sell the tickets they are holding once the game starts they are worthless.
Hold off and you can probably get them for less than face value ... but ... once you do get into the lower section (or any section) ... you can then move to better seats once the game has started.
If you are going to move ... use tact ... not during the first inning and don't crowd the folks who have paid the big $$ ... there are often many open seats (less frequent today) but don't go to see the big matches and I often end up ten rows behind the dugout for under $50.
My former boss loved two things ... The Yanks & The Stones ... don't beech about Yankee prices .... he tried to get me to pony up over $1,000 to see "The Stones" last year. FYI ... you couldn't pay me $100 to go and see them.