Is it possible to have a picklist in data extensions in Marketing Cloud, for example a field called City then users can filter using a drop down and select from London, Manchester or Birmingham?
Unfortunately this isn’t supported as natively as you might want. Even on objects synchronised from Sales Cloud, fields that are pick lists in SC are only provided as text fields in MC.
You will need to do some custom configuration, where you create a separate DE, holding all the options for your pick list fields, and reference it in e.g. Cloud Pages, using LookupOrderedRows to populate drop down input field options.
If this is the use case you are in need of supporting, I can elaborate more on the solution if needed. If you need the pick list values to be available within MC, e.g. when working with Data Extensions in Contact Builder - I’m afraid there is not much we can do there.