You haven't given us much info to go on. How many people are you traveling with? What style of road trip are you doing: hotels/B&Bs, camping, both? Will you be spending most of your time in the car, or will you go slow and take a few days at a time at each location? How much room do you have for a cooler after all other gear? Cool, mild, or hot climate?
In most cases any cheap (or used) cooler is fine. Just add ice every couple days.
If 'roadtrip' for you means mostly driving with a few short stops here and there, and the climate isn't hot, then a 12v plug in cooler may be a good choice. These typically cool 40F below ambient temperature so not a good choice for hotter climes. I wouldn't want to mess with these if spending much time camping.
If you have room (e.g. a van with sufficient cargo space) and you don't mind the weight, then the RTIC coolers are nice, essentially the same as a Yeti w/o the prestige pricing. Just checked and the 45 quart version is on sale for $150, and the 65 quart for $180. We took a 65 on a road trip this summer and it performed quite well in 110F-120F weather, with ice lasting 4-5 days with 4 people regularly accessing it. However, it is large and heavy (extra insulation).