We will be visiting Glasgow the lat week of September, our first visit to Scotland. We are staying at the Grand Central Hotel and would appreciate any tips for day trips, etc.
Will you have a car?
If not, take a look at the day tours offered by Rabbies.
I have taken a couple and they are very good.
A lot will depend on how long you have in Glasgow. Are you there on business, or is it a holiday?
A lot of what you'd want to see on day trips depends on your interests. There's enough to see in Glasgow to keep you busy for a few days, but if you're travelling by public transportation (train, bus), then the best places for day trips would be Edinburgh, Stirling, Falkirk, and possibly Dundee.
New Lanark would be a great place for a day trip, or you could take the train out to Milngavie and hike a bit of the West Highland Way. Or train and bus to Drymen, and hike a bit of the Rob Roy Way.
One thing that you should really treat yourselves to while you're in Glasgow is the Linda McCartney Exhibition at the Kelvingrove Art Gallery.
Do you have Rick Steves Scotland? It has a very good chapter on Glasgow, and you're sure to find something to interest you for a few days.
The one thing he didn't mention that I loved was the House For An Art Lover. Details of this, as well as how I spent the rest of my time there (I had four nights and didn't run out of things to do) are in my trip report from a few years ago; just skip down to the Glasgow sections: https://community.ricksteves.com/travel-forum/trip-reports/uk-trip-report-glasgow-manchester-liverpool-in-september-2016
Of course, Glasgow is a city, so if you're not looking for city attractions, you'll want to go elsewhere in the country. I don't know if you're spending time in Edinburgh as well; if not, note that it's less than an hour from Glasgow, very worthwhile, and VERY different (as different as Baltimore and Washington DC, to give a US example of places that are geographically close but not close in any other way!).