For Glasgow, the obvious choice is The Hilton Garden Inn.
Marriott and Indigo also not too far away and there’s also the old favourite Leonardo’s (nee Jury’s) on Jamaica st.
It’s not that close but can’t be more than a 10 minute walk away.
For Edinblurgh, there’s a Leonardos between the royal mile and Waverley train station where most of the rooms are in a different building from reception, so you can come and go without anyone seeing you.