Minimum duration for a Park Hopper Passport is 4 days. But this is still the best way to go as you can hop between parks and only be docked for that one days usage. A one-day ticket ($46 plus tax) is expensive by comparison and is only valid at one park that one day. No hopping.

Unused days on Park Hoppers never expire (except for special time limited tickets like some Florida Resident tickets, etc.)

If you stay at a Disney owned resort you can get a "Length Of Stay" Passport that is valid from check-in through the entire day of your check-out, and might be a good option if you are stay on property. Disney resort guests also get early admission to the parks on a rotating basis, and guaranteed park admission with valid ticket (which could be a factor around Thanksgiving which traditionally sees the parks reach capacity and stop admissions).