Hi Paul,
I looked at the Imagination and checked out both the state rooms and the pricing. You can do a 4 day cruise on this ship for about $1800 for two people in a balcony cabin. Keep in mind however that this is not all your costs. You will have a fuel supplement on top of that, tips, beverages and excursions, so if $2000 is your total trip budget, this would not be a good choice.
If your wife doesn't want to dine with others there are lots of options for almost all cruises. One is of course the room service option which is what I think you are thinking of when booking a balcony cabin? But there are many other options that don't invlove sharing a table with 6 people.
Manyof Carnivals ships offer a Supper Club, where you could dine every night at a table for 2. More information on their dining options can be found on their web-site. There is an additional charge for this, but you could book a lesser cabin and still come out ahead. I think the charge is around $25 per person per night to dine there. You could dine in the buffet area the first and last night of the cruise and dine in the supper club the other two nights and only add an extra $100 to your 4 night cruise.
Infact almost all the lines offer an alternative evening dining venue, other than the buffet. Celebrity, for example has sit down casual dining where you could reserve a tabel for two. The menu is a bit different than the main dining room, but the extra charge is just $2 per person and serves as tip for the wait staff. Other lines have bistros or other specialty restuarants. Some lines allow you to make a reservation online before the cruise.
You actually have more options than you may realize. You coud contact a travel agent that Specializes in cruises. Make sure you get one that is knowlegeble about lots of different lines, especially their dining options.
A good travel search engine might help you too. I like http://www.kayak.com/cruises
It lets you enter your proposed sailing dates, and other requirements and then shows you all your options. You can then narrow those options down till you find some thing that fits your needs. They have links to web based travel agencies, but you can also just go to the cruise companie's web site or your own agent once you've found what you are looking for.
Good luck with everything and let us know what you end up deciding. We'd love to have you visit our site again.