Why would you take an expensive and time-consuming cab to Yankee Stadium when it's so easy and inexpensive to take a subway?
As for restaurants, remember, this is New York, and there are literally hundreds (thousands?) of decent restaurants a short cab ride away! How about some ideas on price and specific types of food you would like?

Taking a cab to the Stadium is a waste of time and money. There are special subway trains added for Yankee games that go right to the stadium. Also - you won;t be able to get a cab back - there are none in that neighborhood.

And don;t plan on eating in the area - there are few places in the immediate vicinity, mostly of the tavern type. You should really get to the park at least 2 hours before the game - to tour Momument Park and see some of batting practice. Your best (but not good option) is to eat in the park - do you have seats with waiter service?

Also be aware that security is very tight since 9/11, making for long lines getting in; you cannot take anything larger than a regular handbag into the stadium and they examine the contents of many bags.

Sorry - note that car traffic around the Stadium is horrific both before and after games - highways often back up 30 minutes or more so taking a cab will cost a SMALL FORTUNE.

I've taken a cab from the midtown area to Yankee Stadium and it wasn't a small fortune, but you have better luck winning the lottery than finding a cab back from the Stadium. If you take a cab there, be prepared to take the subway back.

I'm not sure if you can tour Monument Park before a game, if so, you'll have to go way early. If you don't care about that then there's no need to get there super early. Have a good time!

Monument Park is open for touring before every game. It closes I think 45 minutes before game time - check with the Yankee we biste. (Since it;s right next to the bullpen they can;t have people wandering there during the games.)

Cab fare depends on how much traffic you're caught in near the Stadium (everyone trying to get into parking lots which clogs the narrow streets). This will be esp bad for a Mets game - which will be a sell out - and when even more people than usual will drive.

I'm with the other posters - don't bother taking a cab to the game, and you surely shouldn't think of finding one on the way back. Honestly, some of the fun is hanging out on the subway back with everyone all hyped up from the game. It can make for a very entertaining ride, particularly during a subway series!

You're staying in a central enough area that I would just scour Zagat or CitySearch to find a restaurant to your liking. You're not giving enough specifics on what you're looking for.

Back to the game - get there early and hit Stan's or one of the other bars beforehand for a beer. They're much cheaper than inside the stadium, and the scene is always a good time.

Any BLT restaurant is a good bet..

Thanks everyone...we'll take the subway. No, we don't have seats with waiter service, we'll figure the food situation out.
Based on the website, there are no tours of Yankee stadium on game days, but it seems you're telling me otherwise. I'll make a call and find out. Thanks for your help!

Not sure if your hotel is changeable but there are several all suite hotels right near that Courtyard that might be better with a toddler. Affinia 50, the Kimberly and the San Carlos are all within a block or so of that Courtyard and have studio and 1 bedroom suites with kitchenettes. A 1 bedroom would give you a place for naps.

Most people would take the subway to/from the game. Agree that you can cab there, just leave plenty of time. There's also a ferry that can be fun on a nice day but it does take longer. I'd only do the ferry one way if you do it.

There are no tours on game day but you can walk on your own thru Monument Park and watch batting practice as nytraveler says. Here's a page with lots of good info for you with links
http://gonyc.about.com/cs/attractions/p/yankee.htm

Some restaurant info near the hotel-

Ess-A-Bagel considered some of the best bagels in NYC is right across from the hotel. Cafeteria style.

La Mangeoire and La Mediterannee are 2
French restaurants nearby that do good prix fixe dinners. (If you eat early-before 7pm-you should be fine with the baby). PJ Clarke's is up the street on 3rd ave. & 55 st. for burgers. BLT STeak is good but pricey. Patsy's on 60th & 3rd would be good for pizza and pasta.
http://menupages.com/restaurantdetails.asp?areaid=0&restaurantid=3464&neighborhoodid=4&cuisineid=50

Most think TOTG is overpriced for very mediocre food. If you go, do lunch which at least isn't so pricey. The Boat House in Central Park is also pretty and better food.

There are no tours on game days since the tours include many parts of the stadium including the club house.

However, JUST Monument Park is open before every game so anyone with a tickets can look at that area. double check the web site but I think it's open until 45 minutes before the game starts.

For a 1:00 day game, you have to be at the last LEFT FIELD gate to enter the Stadium by 10:15am or 10:30am at the latest (for Monument Park). When you get off the subway, left field will be straight ahead & slightly to your right because you will be behind the Stadium. You will see the crowd & there are alot of police officers.

Allow 45mins to an hour to get there, especially if you are unfamiliar with the subway system. Definitely go to Monument Park. It is amazing.

It is very organized but if you are not on time you will be shut out. I am a season ticket holder so take my word for it.

They take your game ticket & everyone marches in together. Once that initial crowd has been admitted, usually there is no further admittance for Monument Park that day. Alot of people get there early.

Bring sandwiches to the game for lunch & definitely take the subway. If you get there to see Monument Park you will not have time to go to Stan's or any of the other bars.