I know some people feel that TS meals take up too much time, but I think that when you have an ADR they actually take up less time than trying to be spontaneous. If you are spontaneous and trying to get in as a walk-in, you may find yourself waiting around for an hour or more, IF a table is even available for walk-ins at all. In my experience, when we had an ADR and got there about 15 minutes before, we were either sat BEFORE the ADR time or at the ADR time. This was in July 2008, not during free dining, but definitely more crowded than January will be (provided they do not offer free dining in January, and I have yet to hear reports of free dining extending beyond mid-December).
It also depends on your dining preferences and how flexible you are about your restaurant choices. If you have your heart set on Le Cellier, definitely plan to make an ADR as soon as you can! Same goes for the castle, breakfast at Chef Mickey's (dinner is slightly easier to get but still difficult), or Ohana. Easier restaurants to get into (most likely, but of course not set in stone) are Marrakesh, San Angel Inn, Nine Dragons in Epcot; Plaza Restaurant and Tony's at MK; Hollywood & Vine dinner at DHS (though I hear the food is terrible); some of the more low-key resort restaurants (Boatwright's, for example). You may find some luck being a walk-in at these.
There are also a TS few restaurants that do not accept ADRs. They are Beaches and Cream at Beach Club (which has very few tables and usually a long wait), Big River Grill on the Boardwalk, and ESPN Club on the Boardwalk.
You could also make your trip more spontaneous by having lunch at a CS restaurant each day you are in the parks. I have done the math with the deluxe dining plan, and even though we decided against getting it (it's just too much food for us, but others really love it), if we did a CS lunch each day on the deluxe plan, we would still save a lot of money vs. paying OOP for all those meals (even before factoring in the snack credits and the refillable mugs). So if you would like to be more spontaneous at least during the day, you could do it this way, and go to TS dinners and breakfasts, or even try some 2TS credit meals. The castle is great for kids, and all the other signatures that accept the DDP have children's menus as well. If you feel your kids can handle it, you could try some of the 2TS places for a couple of dinners. You could also treat them (and yourself!) to a dinner show one evening for 2TS credits!