Sounds like a lot of fun' I'm jealous!

A few helpful points from my view having done this before, but recognising that others have made some of them already:

• As GoSh4rks mentioned, be aware that at certain times, typically midnight but sometimes before in some cities, hotels will vanish from the app (may work via the phone), it doesn't sound likely to be a problem but in case you felt like dinner before the decision then you may be disappointed.
• If you have any corporate codes that you're eligible for they can be very helpful to keep the rates down for last minute bookings like this, even the AA one or M11/M12 Marriott ones are often better than nothing (but do get loaded automatically in the App/Website now I believe)
• Definitely walk-in rates are going to be a lot more than using the app. Note having once done this a long time ago I found that local tourist information offices would often have vouchers for local hotels, including ones like Marriotts, that gave you USD10-20 off, or free parking/breakfast.... not as good as using the app, but better than just walking in
• The earlier you book the higher the chance you have of some pre-arranged upgrade/welcome due to status... if you book in the parking lot then the person checking you in, unless they are the front office manager, will be less likely to upgrade your room (which are often done in the morning of arrival), as mentioned by ElevatorEnthusiast
• Marriott rewards rates are guaranteed to be a few USD cheaper than booking via another channel
• In the past I would have used the website as more reliable, but the app has gotten better... enough to manage this type of booking I feel
• In advance, set yourself a "points dollar target" and then decide to sometimes use points based on that simple calculation (e.g. 1.5c/point), as at the last minute your points could give you a real bargain in some cities - but you don't want to be trying to work that out each day. In this regard, you may find that you can get a cheaper out of town type property and save a fortune, and if you really need a room for the night and arrive after the lounge happy hour and you leave after breakfast, no need for an inner city full-service hotel
• You can end up paying huge roomrates if you get unlucky (e.g. an event or big conference in town) and you aren't flexible - in theory you can check this the night before as you relax/eat dinner, so you may choose to change your destination for the next day if the rates are very high on a single day/week.
• If you haven't already a Marriott credit card will give you bonus points, they may add up

Finally... don't forget that Hilton awards status based on stay... so you could do some nights outside of Marriott and get status there. Certainly relying on a single chain when you're doing this type of trip can be risky, as some towns won't have a Marriott, or the Marriotts may be crazy expensive compared to another chain. If the hotel prices seem too expensive it is good to have a backup chain to just sanity check (Hyatt or Hilton are the typical choices).