I see that some of the other agents suggested a number of the neighborhoods that would be highest on my list for their similarity to Linden Hills. To name a few:
Macalester/Groveland ,St. Paul
(Tangletown within Mac/Groveland)
(Kings Maplewood within Mac/Groveland)
Merriam Park, St. Paul
Highland, St. Paul
Crocus Hill, St. Paul,
Ramsey Hill, St. Paul,
Summit Hill, St. Paul,
North St. Anthony Park in St. Paul
...ok, by now you can see that I like St. Paul.
Bryn Mawr, Minneapolis
Prospect Park, Minneapolis
There are truly great options for you on both sides of the river.
I'm curious as to what the nature of your relocation might be. Might you be working in Minneapolis or St. Paul, or do you have the flexability to work from home? Depending on how long a commute you might be willing to deal with (if you have one at all), you are going to have a lot of options that you would be wise to at least look at long enough to scratch off the list. Also, how long do you think you might be staying in the Twin Cities? (if you can possibly answer that question)
I would recommend that you make some prospecting trips to the Twin Cites and that you head out and look at a number of these areas in great detail with your realtor. I find that most of my transfer buyers look at about 30-50 homes with me in order to get a feel of the market that they are approching, however, depending on how broad your search ends up, you could view even more than that. This process doesn't take as long as you might think as you can see up to about 30 homes in a 2 day trip if you're really on a mission. Best of luck and feel free to contact me if I may be of any assistance. Adam Duckwall, Realtor in St. Paul