Is there an alternative to Synthroid (thyroxine) that doesn't have to be taken daily?

Possible. Levothyroxine (t4) has a long 1/2 life (up to 10 days in new hypothyroidism) so it is possible to dose a higher dose less often (e.g. 100mcg every other day). The problem we run into is compliance issues: many patients tend to forget to take their pills unless it is given once daily.