siargao: there is a dive shop in the permanent market area on the beach in general luna. i forget the name. when i was there in december they could not find a second diver during the week i was there, so can't say anything about either the shop or the diving. there are dozens of places to stay along the beach surrounding general luna. 'motorcycle' rental is reasonably cheap and plentiful. imo siargao island as a whole is one of the more interesting places in philippines (surface wise). it is beautiful, laid back, and friendly. you will likely have the island to yourself at the time you plan to be there. be prepared for rain.
the transportation options in and out of surigao are as centrals says. the ferries to lilo-an, san ricardo (frequent ferries daily), and maasin (south leyte) leave from the main port, about 15 minutes out of the city. if you plan to go to leyte this way, it might be in your best interest to grab the long distance bus to manila, in surigao. the bus originates in davao. ask the driver to let you out in front of your resort, which he is likely to do. worst case scenario you get off in sogod city and take local tranport up the bay from there. the local bus from lilo-an, and especially san ricardo, is slow. distances are farther on the ground than they appear on a map. if you have the time and the patience it is fine, and in any event is completed during daylight. the ferries to and from siargao/surigao are primarily passenger bancas, and leave regularly from the boulevard.
there is a daily cebu pacific prop flight from siargao into and out of cebu. the maximum advanced luggage you can pay for is 20kg. you can buy overage at the airport only, and it is piss you off expensive.
sogod bay: you can't go wrong diving in south leyte/sogod bay. there are several well regarded dive ops there who will take good care of you. my favorite is peter's. from surigao your arrival options are as above. from cebu there are ferries to maasin and hilongos (i think ormoc is too far out and don't recommend it). from maasin it is +/-45 minutes to the padre burgos area, and from hilongos closer to 90 minutes. from manila, fly to tacloban and arrange private transport (about 3 hours). while it isn't the easiest place to get to, no one complains about the diving once there.
davao: why? it's the kind of place to visit if you have friends there, or are on an extended holiday. very extended. that's just my opinion, but if you have your reasons good advice will be forthcoming.
good luck and have fun.