If you are looking for a zombie-proof fortress, few places can compare to an offshore oil rig. Provided you have the means to locate and reach one, you'll likely find them abandoned, since during the early stages of the crisis the crews will probably have left to ensure the safety of their families. You can greatly reduce power consumption and the chance of a fire or explosion so long as you turn off the drilling and refining equipment. The remaining fuel and natural gas should provide more than enough electricity for decades. Rigs are designed to hold crews for months or even years at a time, so there will be plenty of food, medical supplies and full amenities to recreate the comforts of home. Rigs also have desalinizers and purifiers so that fresh clean water will not be a problem for a long time. Being so remote means that you won't have to deal with swarms of desperate, possibly infected refugees. And being on the ocean means you can supplement your food rations with seafood.
There are numerous problems, however, and the aforementioned fires are only the tip of the iceberg (icebergs may also be one of the problems, especially in polar regions). Hurricanes are probably the largest threat, but pirates are yet another problem, so remember to keep weapons and plenty of ammunition, and if you brought large, impractical-against-zombie weapons like a minigun, it's best to leave it out where potential thieves can see it and rethink their options. Corrosion of your equipment is another major worry, and as little else rusts metal faster than a sea breeze. Mother Nature will be your biggest enemy, from stormy seas, to brutal icey winters intensifed by the ocean air (where applicable).
The Offshore Oil Rig is a unique holdout point, though rarely is it accessible enough to be an option. It can be a terrific short term bastion, but for long term survival, supplies will need to come from the mainland. Maintenance of both the facility and the sea vessels may be difficult, but crucial for survival.