Sounds like a great starting point to me
If you learn a wee bit about how to read a smaller river, it'll stand you in excellent stead for the bigger ones. Smaller waters are more intimate and you get to find out about the insects more and where the trout lie as you can see more of the available water and topography of the river bed.
Once you figure it out , the Don or the like will be far less daunting.
the other advantage of staying local is you can come and go as and when you please, so you are more likely to spend 2-3 productive hours once you figure when the hatches are, than spending all day getting hacked off before the fish come on the feed.
Its a lot of fun, I've a small river near me now so this year will spend many evenings out exploring.
I'll make trips to the Don though, but only when i know there is likely to be a hatch on
Should be great fun.
I recommend following some of Robs leads, it'll provide you with a lot of fun, without the driving.
By all means visit the others rivers if you want though, all experience is good, for the Don i'd wait for a summer evening from mid june onwards and come up to fish from 6-11. The evening rises are the best way to find fish and hone when to lift, what flies are on the water and what the fish may be taking (often a wide variety to choose from).
During the Day in May is good too, but you'll find the rises in specific areas on the river and it often doesn't last very long (from 10mins to a couple of hours), can be a bit hit or miss unless someone is with you, still thats all part of the fun
Hope some of this helps
Sandy