First time to Scotland- rent a car for one for two days?

Glasgow is easiest done by bus or train. I would not bother with a car for one day , loads of options to travel outside the city using bus or train. there is the New Borders rail-line all the way to Tweedbank ( about an hour) and the home of Sir Walter Scot,you can aslo get the bus to Melrose from there.
There are regular train to Stirling or down the coast to North Berwick.Linlithgow is a short train ride or take a local bus to Roslin to see the Chapel there.

Glasgow is only an hour by train and it's downtown area is easily walkable, plus there is the hop on hop off bus. For other popular sights near Edinburgh there are lots of day tours, or you can try public transit. I find the day tours are more efficient as they will take you to several sights that might be more time consuming to get to by public transit. I did one that took in Rosslyn Chapel, Melrose Abbey and Hadrian's wall. There are many others that will take you to Stirling Castle and Loch Ness and other places in the highlands.

Agreed you are probably fine without a car.

As just one example of an easy day trip out of Edinburgh by public transport, you can take a bus to Roslyn Chapel and enjoy the village while you're there. Buy a day pass for Lothian Bus and you can use it later in the day to go out for dinner or whatever. (I understand there's also train service to Rosslyn, but can't personally vouch for it.)

no train to Roslynn, might have been one but not since the 1950's

epltd, you might be thinking of the new Borders railway, though some might like to think it goes near Roslynn it really is nowhere near.

Interesting about the Borders Railway, because the Rosslyn Chapel website gives the impression it is near, though it does say you have to take a bus from the Eskbank station to the chapel.
http://www.rosslynchapel.com/visit/getting-here/

https://www.google.co.uk/maps/dir/Eskbank,+Dalkeith/55.8557498,-3.160718/@55.8731509,-3.1626648,13z/data=!3m1!4b1!4m9!4m8!1m5!1m1!1s0x4887beb74498e755:0x260c681aff2bbd31!2m2!1d-3.07845!2d55.88956!1m0!3e3
yes it is about 6 or 7 miles away and takes 30 minutes on the bus, a bus from the centre of the city takes about 45 minutes. I was at the chapel in late March with some friends from Kansas City, they thought it was wonderful and there is a lot of other history in the area including some more modern history as Roslin Institute ,now part of Edinburgh University was where Dolly the Sheep was created.
you may notice various spelling of Roslin ,Roslyn,Rosslyn, they are all used and completely interchangeable you will see all various of the spelling in the village.

I'd get a car to be honest. Driving is relatively easy (after about an hour of realizing how weird it is), but there isn't much traffic compared to say- Los Angeles. If you have a car you could theoretically go to both Glascow and stop by Stirling on the way back. Stirling is beautiful. I found trains in the UK to be a bit of a slow pain in the rear to be honest. Just going to the station, getting your tickets, and getting on, then getting off, finding transport..Its annoying! Spare yourself the 2+ hours of transfers/different methods of transport and get a car. You can get around a lot easier.