Hi, we'll be traveling to Berlin and Dublin around the end of October. Any suggestions on places or things to see around those two cities?
Get used to using TripAdvisor as a research tool.
https://www.tripadvisor.com/Attractions-g187323-Activities-Berlin.html
https://www.tripadvisor.com/Attraction_Products-g186605-Dublin_County_Dublin.html
Berlin has much to do, the Olympic Stadium, great museums (especially Pergamum), Checkpoint Charlie, and much more.
Dresden is an interesting city if you want to do a day trip.
The Rough Guide to Berlin is an excellent resource. RS has a Berlin book now, too.
On this website, there is much info
https://www.ricksteves.com/europe/germany/berlin
https://www.ricksteves.com/europe/ireland/dublin
Click on "At a Glance" for what RS thinks are the best sights in each city.
Berlin has tons of sights in the form of major museums (art, ethnographic, and other) and historic sites with museum-quality explanatory material. I could have spent about 2 weeks there without leaving the city. Consult a good guidebook so you can choose the things of most interest to you.
I can’t speak about Berlin since I have not been, but in Dublin we enjoyed the Guiness Brewery and Kilmainham Gaol. Got tickets in advance for both.
A) Do you mean places in or really ouside of these cities?
B) What are your interests?
In Dublin our favorite stops were Kilmainham Gaol, the Museum of Archaeology and the Trinity College walking tour led by graduate students from the history department. The Book of Kells was somewhat underwhelming but the library was really something to see. And if you have time for a day tour outside of the city I heartily recommend Newgrange.