Alnmouth and Alnwick seem rather close (4 miles from rail station to castle).

i'd rather preserve some flexibility on timing - how long to stay at Cragside, whether or not to visit Rothbury, etc. My main concern is that taxis be available not long after we call, so that we aren't stranded or waiting an excessive amount of time. I should be able to give at least 30 minutes - by then I should have a good feel for how much longer we'll want to stay. I'd guess they'd want something more specific to give a deal, but probably worth checking.