I would vote no stroller... they are old enough to walk. If this isn't the 'trip of a lifetime' (and it looks like it isn't from your sig), have them make choices, slow down, don't rush to do it all. It is liberating not dealing with a stroller, parking it, stopping to get them in, etc. The exercise is good for them and teaches them what a healthier lifestyle is about. At the least, don't get them both in a stroller and give them high calorie snacks... they would get a double whammy of no exercise and instead eating more food. I may not be on the giving end of a 'look', but I would be embarrassed to put an 8yo in a stroller. We have a societal obesity problems and sticking kids at that age in a stroller isn't moving the right direction (not saying your kids specifically are a problem, but it is a societal problem).
bottom line is your kids, your call, but think of the cool things that you could do with that $$$ instead. (ask them if they would rather have a stroller or a nintendo ds and if they don't use a stroller, they can get them.). ? just a thought.