Budget is definitely a concern. Staying in Manhattan?? Good luck unless you are Donald Trump. I live in Central Jersey and can take a few trains and get there soon enough. As for batting practice, it looks like you might be screwed:
Guests are welcome to watch batting practice. Gates open two hours prior to each game.
BATTING PRACTICE TIMES *
1:05 p.m. Game Time 4:05 p.m. Game Time
10:40 a.m. Yankees Batting Practice 1:40 p.m. Yankees Batting Practice
11:40 a.m. Visiting Team Batting Practice 2:40 p.m. Visiting Team Batting Practice
7:05 p.m. Game Time 8:00 p.m. Game Time
4:40 p.m. Yankees Batting Practice 5:40 p.m. Yankees Batting Practice
5:40 p.m. Visiting Team Batting Practice 6:40 p.m. Visiting Team Batting Practice
* Please note batting practice times are subject to change without notice.
This is from their official (http://www.mlb.com
) site. You might only be able to catch the end of it and the visiting team. I rarely hang out at any of the bars but let me know if you want some special places, have a lot of $$, and plan on staying up late.