There is a drink you mostly find around New Orleans called "Herbsaint", which is cheap and has an absinthe-like flavor (no actual wormwood, though). It really isn't bad. It doesn't louche either, but it's a fun drink that doesn't suck. Good over ice or in cocktails
Most liquor stores stock Lucid (green) and Kübler (white) that are not hella expensive $50-60. They are not bad as a starter for someone who has never tried it and Kübler is a regular buy for me. They are true absinthes, made with Artemesia absinthium and without any artificial crap. Lucid is a reverse-engineered pre-ban French absinthe and Kübler is a Swiss LeBleue.