You could go to Alloway, now a suburb of Ayr, to see Burns Cottage. (Frequent train Glasgow-Ayr, bus to Alloway.) It is the genuine house the family lived in. Journey down the coast is under an hour and quite scenic.
But be aware, the thatched cottage is very simple and there isn't much inside. I believe the Dumfries Museum has a lot more content, as such.
The ruins of 'Allowa's auld haunted church' (Tam O'Shanter), and the bridge the witches couldn't cross, are still there. Although Robert himself and wife Jean Armour are not buried in Alloway (Mausoleum in Dumfries), a great many of his family are. That might be of interest to your husband.
Do stop in Ayr town. Look out for the Wallace Tower (Braveheart), and the old bridge that Tam cantered over at the start of his long ride home from market. Flat shoes – beware cobbles.
South of Alloway, still on the coast, Culzean Castle. Remarkable National Trust-maintained big castle with interiors (fabulous ceilings, stairs) by Robert Adam (late 1700s). The coast bus used to pass that way, but you are probably looking at a taxi, really.
Glasgow: Kelvingrove Art Gallery & Museum, must see, esp their collection of Scottish Colourists, and The Glasgow Boys (and Girls).
-- Also the Burrell Collection: I've never seen it myself, always been shut, but I'm told it's remarkable. Near the University.
-- Glasgow Cathedral, built around the same time as the one in Pisa (12thC), but massively different.
-- Tennant's Brewery, guided tours. My son and I took one quite recently. Fun. Stairs are steep. Includes pint of ?strong? lager. (I don't remember, so it probably was.)
-- The Ubiquitous Chip, restaurant, famous, central, good. (Used to be a journalistic long-lunch hang-out.) Will be busy, booking required. Recommended.
BTW: you might check out You-tube for animated films of Tam O'Shanter. There are several. The poem is written in dialect (Lallans), but the films make it clear and funny, in a way that an English-English translation does not.
(Sorry to sound like the Ayrshire Tourist board, but my family are Ayrshire Scots for generations back and we went to school there.)