I'm not sure if you mean you will be staying at one B&B for the entire stay and doing day trips. It often takes much longer than one thinks to drive the Irish roads - about double the time one would imagine.
I am not much of an expert on Irish good food, but the Muckross Park Hotel near Kilarney had some nice meals we enjoyed, but that was quite awhile ago.
We are not a source of B&Bs but check out www.smoothhound.co.uk. That's a great source of places to stay.
My partner and I spent a week in Ireland in September. We stayed in Cork for 3 days, Galway for 3 and Dublin for 2. Cork is a good base for visiting the southwest. You can do day trips and return for dinner in the evening. We stopped in Dingle on our way from Shannon to Cork, and unfortunately Out of the Blue was closed for lunch, but we found a pretty nice pub a few doors down. Dinner at the Ivory Tower in Cork was excellent. Many restaurants are closed on Sunday so the next day we had dinner at the Mustard Seed in Ballingarry after touring the ring of Kerry and before returning to Cork. It was expensive but wonderful. Lunch at the Ross Hotel in Killarney was nice and reasonably priced. Monday we went to Bantry and then to Kinsale, where we had lunch at Fishy Fishy Cafe, which I highly recommend. Dinner at Greene's in Cork was pretty good but did not compare with the others so far (top places in Cork are closed Mondays). On the way to Galway we stopped for lunch at Moran's in Kilcolgan. You must eat here! Absolutely the best seafood we had in Ireland, maybe the best anywhere. The tempura prawns were amazing, and the oysters and the seafood salad absolutely delicious. I also had the best Irish coffee here. In Galway the best restaurant was Kirwan's Lane. Modern cooking, light and delicious. We also liked Vina Mara and Abalone. Galway is charming and a great base for touring the west country. We went to Westport and Sligo (can't recommend any restaurants in either of these, unfortunately). Places we stayed were Lancaster Lodge in Cork, very reasonably priced and in walking distance of restaurants, and the Galway Travelodge, which worked well as we had a car and driving the short distance into town for dinners was easy. You could walk too but it's about a mile. Travelodge is not charming but is very comfortable, spacious, clean and incredibly cheap (use the non-cancellable "saver" rates, and request a family room so you get a sofa, for the same price as a double which only comes with one chair) . Use the money you save on hotels to splurge on meals.
Don't know much about B&Bs but from my limited experience they vary from hopeless to excellent, so take time to research your options. What about self catering if there's a few of you? there's some good deals out there and you can buy some of our beautiful ingredients and do your own thing too.
For a 20 day trip why not break it into two or three - staying in Cork city, West Cork and Dingle itself. It would take hours to drive between these places otherwise.
Cork city is small and very manageable with fine foodie spots like the English Market, Cafe Paradiso, Crawford Gallery. And a drive out to Ballymaloe House Hotel, visiting the distillery at Midleton the same day. I love rural west Cork - try Baltimore, Schull, have a google and see what takes your fancy, west cork is full of great little cafes and pubs and excellent artisan food producers you can visit.
Dingle and its peninsula is a world of its own! Stunning scenery and the Blasket Islands to visit too, great pubs and restaurants in Dingle (An Canteen, Out of the Blue, The Chart House, Dick Macs pub), although not cheap you generally get 'country' portions. So jealous, Enjoy!
We flew into Shannon and visited Limerick, Adare and Dingle last Spring. Lovely trip. Dinners not to be missed: The Wild Geese in Adare, and Out of the Blue in Dingle. Check out Pax House, just outside Dingle, for lodging; Mustard Seed near Adare, many others. An Canteen, a tiny restaurant in Dingle, excellent for lunch, too. As noted, the road system is not 'interstate' quality. You are better splitting your stay between the Adare area, then Dingle, then somewhere on the Ring of Kerry. If you like racing, see if the horses are running at the track between Limerick and Adare; also, in season, first rate rugby/Aussie football at the Muenster team's stadium in Limerick. Look for the Bridgestone? guide to lodging/restaurants in Ireland; sort of like Michelin guide in France. I hope I didn't mess up its name ....
No good info from me on restaurants, but I'm going to second the opinion to stay in a number of places rather than doing day trips from one location. I spent 8 days this fall driving around the south and west of Ireland. I'd suggest picking 3-4 locations and doing trips from each of them. I'd choose Cork area, somewhere around Kerry/DIngle, Connemara and maybe somewhere around Limerick.