We stay at the Bay Club in Waikaloa. The Hilton there is nice, they have their own tram and boats to take you to your room. Their Luau is fine, a bit pricey, if you've never done one.
We have gone up Mauna Kea 3x now, always with a tour. You can drive to the 9,000 foot level in a regular car, then the road is dirt most of the way up. If you go at night, you should dim your lights as you near the visitor's center as a lot of folks are star gazing there, it's really something.
There is a Costco just south of Kona airport, gas is cheaper lines are a bit long. There are some artsy fartsy towns due north of Waikaloa that can be fun. From there you can drive the Kohala Road across that mountain with some great views if it's clear, and then circle back through Waimea. The Waipio overlook is pretty neat to the NW.
The Saddle Road to Hilo is interesting, it goes up 6,000 feet between the two big volcanoes. Mauna Loa is massive, if you can see it. Hilo has some neat restaurants, we like Jackie Rey's. From there you can drive up to Volcano NP, the road around the island to the SE tip is narrow and winding back to Kona. You can see black and green sand beaches that way. Volcano NP will be packed if there is an eruption. The Chain of Craters Road is something to see.
A lot of the island is volcanic wasteland, including around Kona. The Waikaloa resort has anything you might need, there are two shopping centers. I suggest going to "A Bay" Beach at least once. Beware of underwater lava residues that can clip your feet. They have turtles there.
I suggest spending one full day driving around the island, drive to Waimea and the overlook (Waipio) then south the Hilo and up to the NP and then back on the Saddle Road (which is modern). Driving yourself up Mauna Kea is doable with 4WD but not the easiest, you could hit snow in October, but probably not. The sunsets from there are epic. The last time we went we got hit with a blizzard and almost no visibility, the rangers chased us off the mountain early, we couldn't see anything when it hit (December).
You may hear about Hapuna Beach, it's "nice" but not spectacular IMHO. The coffee plantations could be of interest near Kona. Kona coffee is good, but not terrific IMHO. There is a farmer's market in Kona some days where you can buy coffee much cheaper than in shops. Kona is interesting, touristy of course, home of the Iron Man. I don't think whale watching happens in October. They have a lot of things like parasailing in Kona on the bay and fishing trips. We rented a boat one time and took it down to Captain Cook Cove.
You won't have rain in Waikaloa, you likely will in Hilo. My wife adores the place, we usually go for two weeks every other year in December. Our kids often join us as they mostly live on the west coast. A two bedroom condo is a good deal off season, and it's a time share for us.