We are in love with the Big Island and are regular visitors so this post is Big Island answer heavy
I am not sure how much time you have on Big Island but if you are hiking and nature lovers be sure to spend some time in Volcanos National Park. If you are looking to do some lava viewing at dusk or in the dark keep in mind many people will overnight right in Volcano Village because it is a long roundtrip drive to the Kona side (if that is where your hotel is)
https://www.lovebigisland.com/hawaii-volcanoes-national-park/
In Waikoloa, just north from Kona about 20-25 mins, there are very cool petroglyph lava trails. Not really a hike but wear proper shoes and bring water, the sun can be brutal on these as there is little shade.
https://bigislandhikes.com/waikoloa-petroglyph-preserve
The black sand beaches are unique and fun to see. There are few but this one is pretty popular
https://www.gohawaii.com/islands/hawaii-big-island/regions/kau/punaluu-black-sand-beach
If you are into serious hiking, you might want to consider Waipi'o Valley. I have been down into in and played at the beach there, it is pretty incredible.
https://bigislandhikes.com/waipio-valley
Hapuna beach is one of our favourite beaches anywhere. It is well worth spending a full day or at least an afternoon. The sand is powdery soft, the water is clear and fairly warm because it is a long shallow entry into the ocean. If you turn around and face the island in the winter you can sometimes see the snow on top of Mauna Kea.
https://www.gohawaii.com/islands/hawaii-big-island/regions/kohala/hapuna-beach-state-park
Seeing that you are foodies, you should try to take the time to go to a Farmers Market on at least one of the islands you visit. The fresh fruits like papayas, pineapple and mango are so juicy and sweet. I bring a cutting board and a sharp knife in my carry on so we can eat fresh farmers market fruit in the condo or hotel room.
You could also try a coffee farm tour and one of my all time favourite Big Islands activities is the Hamakua Mac Nut tour. It actually isnt even a "tour" so much a sampling room and windows into the production area but there are so many different nut samples to try, plus incredible local farm kona small batch coffees to sample as well. The prices are really cheap and we bought some amazing coffee beans there that we could not buy anywhere else. I was reluctant to go the first time, I thought it was a tourist trap but we had been at Spencer Beach park, which is right around the corner.
https://www.tripadvisor.ca/Attracti..._Nut_Co-Kawaihae_Island_of_Hawaii_Hawaii.html
https://www.hawaii-guide.com/big-island/beaches/spencer_beach_park
There is sooooo much to see and do in the Big Island, I could go on and on. Feel free to ask if you have specific questions
As far as Maui goes, I find it kind of busy and touristy but there are lots of great things to see and do.
Some highlights of our past trips have been:
Rainbow eucalyptus trees
https://www.tourmaui.com/rainbow-eucalyptus/
Lahaina town, especially strolling on art nights
https://www.gohawaii.com/islands/maui/regions/west-maui/Lahaina
Snorkelling in and around Kapalua/Napili
https://napilisurf.com/snorkeling-near-napili/