As a mountain biker, I would go +1 on the mtb option.
Whether road, or MTB, there are load of quiet country roads, and given its size, you are never far away from a small town or village, to get you bearings again, so no real need to have a pre planned route. You could do a full lap of the island in a day, or split north and south over a couple of days. If mountain biking, you could spend a week here, and still not get around to every trail. If you decide off road, try http://www.loaghtanloaded.com or http://www.manxmtb.com websites for social rides, they have one each weekend, and most evenings.
For accommodation, loads of old Victorian hotels on the main Douglas promenade, which is just minutes from the boat. Try http://www.sleepwellhotels.com they used to sponsor the IOM e2e race, and have storage, or http://www.welbeckhotel.com. They are just off the main promenade, but have a good restaurant, and just a few mins walk to local bike shop.
If you want any further advise, just contact me, and if you decide on bringing MTB’s I can try and sort out some trips out.