Do I offer to drop my date home or walk them home?

If the date has gone well and your date has no pre arranged travel arrangements, then there’s no harm in casually offering to drop your date home or walk them home, obviously depending on where you both live. It’s completely their call whether they choose to accept. Don’t push it though, they might just feel it’s a bit too soon to be seeing them home or they might want to get to know you a little more before you find out where they live. Maybe just say it in a way that it doesn’t put them on the spot; simply ask if they’re okay getting home and you don’t mind seeing them home if they’ve any concerns.