I would highly recommend the bike ride, if you're up for about a 6-mile ride (12 miles roundtrip). It's a really nice ride with interesting scenery, and most of it is on a bike path that is separated from traffic.
From Town, you can either follow Main Street to Madaket Road and then pick up the bike path, or loop around via Cliff Road (longer, but scenic) and join the path there.
Taxi fares on the island are set by zone, not on the meter, and apparently the one-way fare between Town and Madaket is $18. You should have no trouble getting a cab for the trip out, but you'd probably want to pre-arrange your ride back (or have of the cab company phone numbers in your cellphone).
I just remembered that you talked about being there for sunset, so I should probably amend my advice -- if you're planning to bike back to Town after dark, you should be absolutely sure that your bike has a working light and reflectors. If you're not used to biking at night, consider biking out and then taking a taxi back. Transporting a bike by taxi is not uncommon on Nantucket, and this list will help you find a taxi company that can accommodate you:
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