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Once in a while, it's nice to slowly sip a drink other than beer.
Literal
Once-in-a-while beer other-than [genitive-の] honorific-sake [object-を] tinily-tinily lick [nominalizer-の-also-も] good [conjecture-でしょう].
ちびちび is a 擬態語 for small, repeated, slow actions — here for sipping a drink slowly and appreciatively. 舐める ('to lick') is used metaphorically for sipping/tasting, especially small amounts savored. お酒 is the bikago-honored form of 酒, meaning alcoholic drinks generally (not just sake specifically, although sake is also お酒). The whole sentence is a leisurely recommendation.