I live in a big city: São Paulo, Brazil. I would like to build a simple telescope dome to do some amateur sky obseravtions. But the whole project lies on the viability to see something interresting more than just some stars. Due to high luminosity of cities this is a good question to ask. So, which physical parameters are relevant to decide if a backyard observatory is a good holiday DIY project?
Many astronomers are using electronic eyepieces to overcome light pollution. You may want to see what these devices can do in your area'
I use several of the Mallincam cameras in my observatory.
Some photos of my observatory and assistants
More home observatory sites
You've identified sky brightness as a potential concern for your observatory project. In that case, you should start by trying to measure it. Unihedron manufacturers sky quality meters that you can use to get scientific measurements in mag/arcsec2. This could give you a baseline for your considerations. You could roughly convert this measurement into a class on the Bortle scale. (But keep in mind that the conversion is approximate.) You could research whether the objects you might be interested in could be seen under that class of sky. More simply, you can use this site to see a map of light pollution in your area. Keep in mind that this map is generally accurate, but may be somewhat inaccurate at your specific location (as there are a huge number of factors that might affect sky brightness). You could, of course, buy a telescope and try to observe objects of interest with it. This would be the most direct way, obviously, to determine this project's feasibility in terms of what you're interested in observing.
I'm sure you realize that such an observatory should not be directly in the path of any artificial lights. It should be (obviously) on flat, sturdy land with an unobstructed view of the horizon. If you're asking specifically about building the dome itself, I have no experience with it. Someone else would have to add information form their experience.
I hope this helps.