Hi, 3rdCoastHighlander,
Allow me to add my tuppence to this discussion.
First of all, I am in complete agreement about not driving in Edinburgh and Glasgow. It used to be fairly easy, at least back in the day when I first started visiting Scotland. However, it is now just frustrating and expensive. Between dedicated bus lanes, bicycle lanes and unsympathetic traffic wardens, the two cities have become very unfriendly destinations for those who choose to drive into their interiors. Added to that, streets frequently change names within the space of a city block. Edinburgh is notorious for that. Parking is an expensive nightmare in both cities. Parts of Glasgow where I used to park for free now have paid parking. So now I not only have to pay, but also to worry about getting back to the car before time expires.
Having said that, if you do want to take day trips to Stirling, or Falkirk or Croy for the Antonine Wall, then you may want to have access to a car. You only want to do this if your lodging in Glasgow provides free parking, and you also want to be absolutely sure of your route in and out of the city. Once you park at your lodging, leave the car there until you are ready to leave the city, and use public transportation until you do. The same applies to Edinburgh. Again, the public transportation is excellent, and trains regularly run to all of the above-mentioned towns. Stirling Castle is about a 20-30 minute uphill walk from the train station, although it's downhill on the way back!
Public transportation in Glasgow is excellent, if they're not on strike. The underground (Clockwork Orange) will take you to Govan. Scotrail will take you to Pollockshields and Cathcart from Glasgow Central. Bus service is excellent, and of course there are always taxis. An all-day Glasgow Tripper card for the buses runs about 3 pounds. An all day pass for the Clockwork Orange is a little over 4 pounds. There are all day bus passes for Edinburgh as well.
As others have mentioned, the best places to visit the Antonine Wall are at Tamfourhill/Camelon, just past the Falkirk Wheel. There is also a very good section on the grounds of Callendar House in Falkirk. Another good section is at Croy (accessible by train from Glasgow and Edinburgh). The WalkHighlands website offers an excellent walking trail for the Croy section of the Wall. Look for "Croy Hill and the Antonine Wall".
As far as pubs go, the best (and among the oldest) in Glasgow are the Clutha in Bridgegate (now reopened after a tragic accident in 2015), and the Scotia Bar on Stockwell Street. In Edinburgh, the Sheep's Heid in Duddingston claims to be the oldest pub in Scotland, while the White Hart in the Grassmarket boasts of its age. Sandy Bell's, in Forrest Hill, is a grand old pub with regular traditional music sessions.
Have a wonderful time, and good luck with your genealogical research!
Mike (Auchterless)
p.s.: Once you arrive in Glasgow, get a copy of the Glasgow A-Z. The paperback book sized one is a lot easier for carrying in a pocketbook or backpack. All churches and cemeteries are marked on the pages. If you want to get a copy ahead of your departure time, there are several used copies on eBay. Make sure that you order the paperback edition, not the large format or spiral bound edition.