We will be flying into Glasgow and staying in Edinburgh, and probably won't rent a car. I have read the best way to get to Edinburgh is by taxi to the Glasgow RR station, then train to the center of Edinburgh. Does anyone have a better suggestion?
There are also regular airport buses from in front of the terminal at Glasgow that drop off at the rail station.
The same bus goes onto Glasgow Bus Station where there are regular coaches to Glasgow that are significantly cheaper.
Worth identifying where your hotel is, as there are opportunities to get off both train and bus before the terminus in the centre.
On a 6 hour layover at Glasgow airport took an easy and cheap bus ride from in front of the terminal which took us into Edinburgh. Enroute, just outside the Edinburgh city centre, in a quasi-residential area, went by several blocks of B&B after B&B, all within easy walking distance of all the Edinburgh sights. My Irish colleague said he always stayed in B&B's in that area and you might want to check location of your accomodation and where best to get off the bus. In our 6 hours we were able to visit the Castle (didn't take the tour), walk the Royal Mile to Holyrood (lunch on the way), strolled through the gardens below the castle, visited High Street and did some shopping with plenty of time to get back to the airport and our flight to Amsterdam.
Don't bother with the taxi. I've not taken the bus direct to Edinburgh, but I've taken the bus straight to the train station where I've caught a train to Waverly Station. I've been in Edinburgh within two hours of arrival from the States. There is an information booth in airport immediatley after you clear customs. You can buy your bus ticket there and they'll direct you to the bus. They can probably tell you about the Edinburgh bus as well.
Thanks, everyone, for your helpful responses.