When normalizing a relational database, should multiple "type" tables be combined into one?
I would go for separate tables for each type.  With so few rows performance will not be a consideration either way.  Individual tables will only have a page or two each.  Similarly for the combined table.

Either way you will have to join a "type" table to complete your views.  Inserts are infrequent at this level of abstraction so locking is unlikely to be an issue either way.

For me, though, having different tables keeps logically distinct items separated, which is a cleaner design.

There will be many different tables which will have a relationship to a type table of some sort.  If there are many different type tables the foreign key relationships are self-documenting and enforcable through DRI.  With one combined table it is difficult to use DRI to say "Venue.TypeID comes from Type.TypeID but only if the Type.Category = 'V'", for example.  The complementary side of this relationship - "Type.TypeID with Type.Category = 'V' can only be used in the Venue table" - is also not supported in any RDBMS's DRI that I know of.