How do you setup a route?

Yes, what you have described is a route, probably something a sales or delivery person would use. The most common route is from your starting point to the destination using specific roads or bridges.

How you set routes depends on the unit and software available. Some units allow routes and they can be mapped out using the Garmin Mapsource program. Some units do not allow routes, but will accept a destination and a waypoint.

If your route changes, try setting the final destination and then set the first waypoint (or stop) by pressing MENU, Where TO, set the location and ADD AS WAYPOINT. When you reach this waypoint, then set the next and so on until you have made all the stops needed.

The nuvi 260 does not have the ability to store routes on the unit.

The best you can do is to add a viapoint to your active route.

I don't believe your unit does routes. You could create a group of waypoints (favorites) and select them as you go.

You could also setup a POI file with all of the stops and use that to select from as you go.

My Nuvi660 isn't able to do routes, but am wondering if the newer Nuvi700 series have this feature?

Per Garmin's page (Plan ahead)
https://buy.garmin.com/shop/shop.do?cID=134

All the 700 series contains this function. There are 12 units that does this in total.

When I did a tour of National Park sites in the SE last year, I programmed about 2 dozen sites into my nuvi 200. I did so by finding each site so they would be stored in Recently Found. Then, with my final destination set I simply selected the next site on my list and set it as a via point.