The Collaborative International Dictionary of English v.0.48:

Ideally \I*de"al*ly\, adv.
   In an ideal manner; by means of ideals; mentally.
   [1913 Webster]

WordNet (r) 3.0 (2006):

ideally
    adv 1: in an ideal manner; "ideally, this will remove all
           problems"

Moby Thesaurus II by Grady Ward, 1.0:

23 Moby Thesaurus words for "ideally":
   absolutely, at best, completely, entirely, faultlessly, flawlessly,
   fully, hypothetically, immaculately, impeccably, in idea,
   in the abstract, in theory, infallibly, just right, on paper,
   perfectly, purely, spotlessly, theoretically, thoroughly, totally,
   wholly