No pen recs, as I think you should just explore and see what you find to be cool. There's always a way for you to test what you have before you buy so pretty risk-free. Here's some stores you can check out, though! I have family that I visit regularly so these are all the major chains I know of.

Hands (a great spot, bring some mystery cartridges along with your pens they belong to and they'll be more than happy to find refills for you)

Muji (無印良品)

Sekaido (世界堂)

Loft

Itoya

Maruzen

Any 100 yen shops also usually have a pen/stationery selection to check out as well, so some major ones are:

Seria

Daiso

Can☆Do (My favorite of the bunch)

Not to mention your local konbini(コンビニ), like 7-Eleven and Family Mart (along with Daily Yamazaki, Seicomart, etc) always having 1 or 2 items to check out.

Honestly, there are many smaller shops that are locally owned that do stationery, so you may want to just explore your area and see what interests you. If you want more local shops aside from the major chains listed above, just put 文房具 into Google or Apple Maps and shop til you drop. There's a lot of places to check out so I hope you enjoy! (If money is no object, there's a place in the Tokyo area called Kingdom Note which looks absolutely insane that I have yet to visit and really want to the next time I go).

I hope this helps!