We hadn't intended to go to the Palazzo Vecchio initially, but found ourselves with some free time and decided to give it a whirl (it helped that the entry fee was covered by the Firenze card).
Having been, I'd definitely recommend it! The inside is stunningly beautiful, starting with a lovely little courtyard just as you walk through the entrance. The highlight is the room on the first floor (Salone dei Cinquecento) with its ridiculously ornate ceiling, but the rest - including the apartments upstairs - are also worth a look.
You can also climb the battlements (your ticket has to include this, it is free with the Firenze card) for a slightly different view of Florence.