I am on a cruise that has a stop in Aomori. The things I want to see are the Museum with the festival floats, the castle and the area around it. I can't tell if it's in the city center or outlying. I would rather DIY, not only because of cost. I just like to do things at my own pace, but I'm traveling alone, I don't know Japanese, so how hard will it be for me to get to these places without a tour? Thanks in advance. Mary

1) The Museum with the festival floats - take a look at the Aomori info on the Japan-Guide, https://www.japan-guide.com/e/e3750.html
On the #3 of the Top Attractions is a link to Netuba Warasse Museum. I am not sure if this is what you want, but if it is, click on that link to see more detailed info and access. The museum is within walking distance of the Aomori city center.

2) Castle - I guess you meant Hirosaki Castle? https://www.japan-guide.com/e/e3701.html
Click on the Hirosaki Castle link to see more detailed info.
Take a JR (Japan Railway) train from Aomori station to Hirosaki station, and then from there take a taxi to the castle.
One-way train is about 40 minutes. For train schedule, look up HyperDia | ???? ???? ??? ???? ??? ???????
And here is a blog found on the internet from a cruiser who made a DIY trip to Hirosaki castle from Aomori:
Precious Memories: Aomori, Japan

I took exactly the tour you described from the Diamond Princess and thought that it was worth the money. It took us through the countryside from the ship to the Nebuta Festival Museum, which was colorful and worth visiting (also try the apple ice cream there). Then we went on to Hirosaki Castle. There was adequate time at both places to visit at a leisurely pace. To cover that much ground on your own, you will have to be very careful to make it back to the ship on time. I'd opt for the tour. Book early as the tours sell out quickly, much as the cruise does. The Japanese love the Princess cruises around Japan.