I'm looking to build a tower. The main room will be my bedroom. Is there any item or spell which would create permanent portals to extradimensional spaces? I'm digging the idea of having doors on each floor that seem false: they open on the brick wall, but when accessed properly give to different rooms e.g. kitchen, library etc.

I've found Demiplane, yeah. Reckon I'll work with the DM to use that.

Guards and wards spell gives option to make illusions over doors to make it appear like they are not there while also applying Arcane Lock. You, those who you designate and possibly those you provide a password to will see the doors and can open them fine. Others see walls and even if realising its illusion, will struggle to open the door.

Galder's Tower creates a tower, your DM might let you use something fancier to move between levels like a sigil that teleports you up/down.

Magnificent Mansion lets you make a mansion in an extradimensional space and you DM could allow you to set up all sorts of things. 

Quote from Cyb3rM1nd >>

Guards and wards spell gives option to make illusions over doors to make it appear like they are not there while also applying Arcane Lock. You, those who you designate and possibly those you provide a password to will see the doors and can open them fine. Others see walls and even if realising its illusion, will struggle to open the door.

Galder's Tower creates a tower, your DM might let you use something fancier to move between levels like a sigil that teleports you up/down.

Magnificent Mansion lets you make a mansion in an extradimensional space and you DM could allow you to set up all sorts of things. 

 Thanks, good suggestions there.