GrandmaSusan: I finally met your son and family yesterday but not in Talkeetna. They have a booth at the State Fair in Palmer where I spent the day with my family. LOL Small town but I still don't know everybody! Their booth had some great stuff.
RhondaK: The length of your trip really depends on how many "side trips" you might want to do and how far you want to travel throughout the state. If you want to go guided fishing, plan a full day or 2 or 3 for that. And keep in mind that salmon have a "schedule" so certain species of salmon will only be in the rivers at certain times of the summer and in different parts of the state it is a different time. It takes a while to swim out of the ocean and make it up the rivers to spawning grounds. So King salmon fishing on the Kenai is earlier than King salmon fishing here in Talkeetna. Also subject to change per Fish and Game regulations.
Flight seeing trips are usually a couple of hours but you may have to wait for the weather. Hiking, ATV trips, museums, shopping or whatever takes time. And as MarleneC said travel can be slow with our 2 lane highways, minimal passing lanes and lower speed limits.
As far as best time of year, it's more of what you want to do than anything else. In my area, the tourist season starts on May 15th and goes to about the middle of Sept. At least that is the day that the bus tours and big hotels officially start. That doesn't mean things close up but they may have limited staff. Lots of college kids work up here for the summer and leave in Aug. for the next school year, but you never know.
As far as the weather, it's a crap shoot. Some years May is the nicest weather but we might still be melting snow. Or getting new snow. June can be truly beautiful but I'm still waiting for the garden to thaw out so we can plant. July has been known to rain the entire month, but this year it was pretty good. Aug. is the start of hunting season in parts of the state so you can all ready feel the cooler autumn air and notice a few colored leaves on the ground. But Alaskans don't NOT do things because of the weather (except flying). Just add a couple more layers and keep going!
In case you can't tell, I use to work at a Visitor Center in our area, so I've answered a lot of traveler's questions. It's been over 20 years ago, but some things never change!