Separetly, not sure why you decided to stay in Yonkers - but assuming it is cost - post info on wher

If you are staying in Yonkers all 3 nights and plan to go into NYC each day, please plan for the commute. You need to check what options are available (bus, train etc) and how often and how late they will take you back to your hotel. Some areas of Yonkers are not very pleasant.
From there you will have to take either Metro North RR or Express bus (I don't know the cost - but not a city bus) back and forth every day. You should be aware that if you have any evening activities planned getting back to Yonkers can be a PIA (after travel in costa rica 10:30 or 11 pm the trains and buses run very rarely - it's not like the NYC subway that runs all the time).
I would not waste time on a tour - you do;t have much and should head straight to what you want to see and do - and do it. If you take the 2 hour Circle line tour it will give you an overview of the outside of the island - but I reco Top of the Rock to get a better overall view - at least of midtown and upper east/west sides - and some of the biggest buildings downtown.
Separetly, not sure why you decided to stay in Yonkers - but assuming it is cost - post info on where you will be so people can comment on safety. Also help you figure out the cost of commuting in and out of the city.
The most popular bus tours are the Grayline hop on/off. But if you're visiting when weather is cold, its not a great idea because the top of the bus where you sit is open. Onboardtours.com has closed heated buses and guides that stay with you. Realnewyorktours.com use subway and walking to get around.
I picked Yonkers off of the map because travel in costa rica hubby wants to spend some time in his former neck of the woods - the Bronxville area. I would love to stay in Bronxville, but am afraid it will be too expensive. Any tips on where to stay in that area would be great - especially if the mass transit is good.
I don't know what hotel/motel you picked, but I don't think there are really any good ones in Yonkers. Mass transit is not really good in any of the suburbs. travel in costa rica You can get to NYC like many commuters do, but it will take time and money and the timing may not work well. Don't forget that you have to get from the hotel you pick to the train or bus station, and parking may be a problem for that part.
I think you really need to give this some more thought if you want a smooth trip, If you want to spend a day or so in the suburbs and visit Bronxville, I would stay in a town that is safer and has some things to see. Yes, it will cost more than a side of the road motel in a less desirable town. Tarrytown and Rye are 2 places that have some chain hotels that you might be able to get in your budget using Priceline travel in costa rica or Hotwire or some other deals you could dig for.
Staying in Yonkers to visit NYC is also not a great idea as we have mentioned above. You'd be staying someplace not so safe, not scenic, and not convenient. I'm sorry to be so negative, but it's hard for us to see your plans working out the way you want. Please consider some compromises. Perhaps up your hotel budget for a day or 2 and save money by not taking expensive tours of NYC when you can see and do so much on your own for much less. The difference may not be so much (some of the tours suggested can be $50 per person and more) The time you'd save coming to and from the city must be worth something too
The only hotel I know of in Yonkers is the Hampton Inn and it's ok but there's really no good reason to stay there to visit NYC. There are no hotels in Bronxville. travel in costa rica If you dont want to stay in Manhattan, at least pick an area on the subway system rather than needing a commuter train. What about Brooklyn or Long Island City?
I can't help on the safety question about Yonkers. And, while I probably wouldn't choose travel in costa rica that Yonkers option for staying during a visit to NYC, I will disagree with some previous posters about its convenience. Train service to and from Yonkers is excelllent and frequent. And, it's only about a half hour train ride to the city. Further, there is service to Yonkers from NYC up to just before 2 a.m. daily
While Yonkers is not far from the city on Metro North the trains do NOT run that often at night, Plus if you stay in the city for dinner (and I can;t imagine eating in Yonkers) by the time you're done you may have to wait 30 minutes FOR a rain, then 30 minutes on a train, travel in costa rica then find a cab to get you to your hotel - so 1.5 hours from restaurant back to motel.
Trains from Grand Central to Yonkers are every 30 minutes at most and the RT fare is about $20 per person. So for a couple you are paying $40 per day for train plus cabs to and fro the train station (I would NOT walk around in Yonkers after dark.)