I don't think it will matter much what color or pattern you paint your hive in a city yard, ...usually not hit by the sun all day long. Still, keep the hive in a sunnier spot, this will lessen the mold issue in hive. In link is a thread on painting. Regarding your dog, time will tell, I had some bees in my backyard with dog and wasn't a problem.
What you could do if it doesn't work out, build a wall with sheets of plywood about 5' tall on the entrance side, bees will have to take more a vertical approach to your hive. Not sure which side you are facing, you can try first without a wall by facing the entrance 180degree away from the dog walk...which could be north or any other direction, preferred facing is south, but that might not be possible in you yard?

Here is a link that might be useful: Color

Thank you for your suggestions- glad to hear your dog had no problems with your bees. I do have a golden raspberry planted near the front (faces east) which should get rather large and two high back chairs that will deter her; I know she would sniff if given the chance she loves honey. The hive receives plenty of sun from 8:00 to at least 3:30. I can't turn the hive to face south as it is on the neighbor's fence line (have written permission from all neighbors) as I don't want extra bee traffic for them. I have heard rubbing lemon balm on the inside of the hive is soothing to bees; has anyone tried this or recommend doing this?

I only know of lemon oil I use as a swarm lure, a couple of drops inside
a box.
A aggressive hive can be dealt with re-queening...I have never done it or
there was never a need. I had some temperamental hives....usually Italian's, it wasn't all that bad, but it seems these were my best hives bringing in the most honey. After a season or two when she get's superseded, it usually got better.

I rubbed lemongrass essential oil in the interior of mine. Here in cold Maine (I'm a brand new beekeeper as of two days ago, in fact, so you can ignore my advice.) I was advised to paint the roof of my hive a dark color. One is some environmentally friendly black paint called Mystic? or something and the other is painted a low VOC dark green paint. I painted the green hive yellow on the bottom and it looks a little like a John Deere tractor---not the unobtrusive look I was aiming for.

I kind of enjoy seeing the white hives from any room in the house. I have a large, elaborately landscaped garden (my own work) but I like the beehive just as it. It's what it is, and I have to say, I am proud that I keep bees. It would be different if I were hiding it from the neighbors. Besides, I notice the weeds less when I'm looking at the bee hives.
mt

Mine:
{{gwi:429446}}

I primed my hives with a high quality oil base paint. It was very humid & took almost a week to fully dry. I thinned it with an additive called penetrol. The finish coat is almost a military green & the color choice was based on the price. I asked the local Sherwin Williams store what he had in the screw up dept. meaning paint that had been ordered & mixed & the customer did not like the color or was simply never bought. I got a gallon of their best oil base paint ( over $40.00 retail ) for $3.00.