Adam Garrett
Extended Stay Hotels

Image courtesy Fords Colony Marriott in Williamsburg, VA
What to Look for in Your Room for an Extended Stay
I recommend checking to see that your hotel has free wifi, a refrigerator/freezer (& be sure to check for or ask about the size), microwave, (even if not standard sometimes hotels can provide them to your room at no cost to you as happened to me in the past week at the time of this writing) if you currently have status or are close to having status with the hotel chain (ask Adam for credit card options that can instantly get you status with your preferred chain,), & the occupancy level you need for your family. You may potentially also check to see it has a stove/oven, a business area, as well as laundry on-site including the costs (though laundromats are an option as well).
Reviews
I also recommend checking reviews on Tripadvisor & especially Google Maps rather than the hotel's website when finalizing a decision between differing options.
Club Level
Club level (concierge level with Marriott) is another factor to consider, especially if you have status with a chain or could attain the status needed for free access. In upper-end hotels, club level could mean 3 meals a day. While they typically advertise breakfast and snacks but don't advertise lunch or dinner, see my review of an upper-end hotel that didn't advertise either lunch or dinner but had fantastic meal options in each case. Be sure to watch out for some that are closed on weekends and holidays.
Status
[even if you don't already have status, for most of these options, there are credit cards that can get you status with the hotel chain almost immediately if not immediately, which can be very valuable prior to a stay (potentially saving you hundreds or thousands). The only status that Adam has with hotels is through credit cards, not by meeting the usual stay requirements (I have Hilton Gold, Marriott Platinum, Hyatt Globalist, IHG Platinum, Raddison Gold, etc. as of February 2021. With that status I get extra perks, depending on the brand, property, and status level. The best status I have from a credit card is Hyatt Globalist status, which gives free breakfast at most brand locations that don't include it as standard or free club lounge access and space-available upgrades up to standard suites. While I don't have it, there are solid ways of getting Hilton Diamond status through credit cards and many other options unmentioned - let me know if you'd like to know more about obtaining status through credit cards)]
There are also solid options with points & free night certificates in many areas including SE VA like the Fords Colony Marriott in peak season & 2 bedroom options with Choice in Williamsburg as well.
Hotel Brands Good for Extended Stays:
Marriott
Residence Inn by Marriott (free breakfast & full-sized refrigerator, stove, microwave, coffeemaker - 1 client of mine enjoyed his stay here near Patrick Henry Mall)
Towneplace Suites by Marriott (free breakfast; full sized appliances, cookware, dishes)
Fairfield Inn & Suites (free breakfast, minifridge & microwave)
Springhill Suites (free breakfast, minifridge & microwave)
Marriott Vacation Club - Marriott's Manor Club at Ford's Colony in Williamsburg only, which my wife & I have enjoyed (we have tried the villa & the guest room), offers good amenities for extended stay if opting for the 1 bedroom or 2 bedroom villa (the guest room that is not a villa doesn't offer a full kitchen, but still offers a microwave & minifridge)
Marriotts with Concierge Levels if you have free access via status or think an upcharge for it would be worthwhile. Examples include Newport News Marriott at City Center, Sheraton Norfolk Waterside
IHG
Hilton
Homewood Suites (Free breakfast - Williamsburg, Greenbrier, & near ORF (Norfolk/Virginia Beach))
Hiltons with a Club lounge if you have free access or would prefer to pay extra for it like Hilton Virginia Beach Oceanfront, Hilton Norfolk the Main, etc.
SE VA Hotel Examples
Low End
Weekly rates starting at $240. See examples in Hampton Roads here, but be sure to check the reviews. For instance, they have locations in Newport News (is 3.3/5), Hampton (1.9/5), Norfolk (1.5/5 review on Expedia), & 3 in Chesapeake starting at $230 (Sun Suites 2.8/5). Also availability can be limited. The Mulberry Inn is an additional option with better reviews than any of those options while not being much more expensive than them. Extended Stay America has cheaper rates for those staying 60 nights & more.
Middle & Upper End Hotels
See my article on the subject here.