Someone at the University of Maryland Center for Environmental Science has created an interactive map showing what the climate in many cities is expected to be in about 60 years and then gives the closest analog of that future climate.
For instance, Portland’s climate is going to be similar to today’s climate in Shingletown CA.
It’s not clear if they are taking into account changes in the coastline, a lot of plains will probably turn into marshes which should affect the humidity levels.
D.C.'s climate in 2080 is going to be similar to the current climate in the Shreveport (LA) area…but I don’t know what Shreveport is like right now, so this doesn’t really help me. Plus, in 2080 I’ll be long-dead. 
From a quick look, they appear to be only considering temperature increases and vegetation changes. There is so, so much more to rapid climate change than that, like the general destabilization of the climate system, leading to more powerful storms and sudden and severe microclimate changes, the migration of invasive species, large-scale crop failures to due floods or drought, and many other unpredictable changes.
One needs to be very cautious about just thinking, hey, it’s gonna be warmer! This is especially a naive tendency for those living in more northerly climates who tend to think “warmer is better”. Maybe it is where you live, but with the unprecedented suddenness of “warmer” relative to the earth’s natural climate cycles will inevitably come some number of undesirable and even dangerous changes that no one would have wished for.
For example, right now where I live in the Great White North, “warmer” means stifling heat, a very unusual period of drought, and massive wildfires.
Another, mostly-separate, climate issue that’s mostly overlooked is the water crisis. A lot of the developed world gets their freshwater from underground aquifers that are replenished much more slowly than they’re getting depleted. Even without global warming, that’ll be devastating to, for instance, the American West, within a few decades.
It’s not clear what that app is based upon but the National Climate Assessment provides a high resolution (down to the county level) “best guess” for the United States. There are additional tools using the same data at lower resolution and confidence for the rest of the world.
Although sea level rise is a component of the consequences of climate heating most places that are not directly on a low-laying coastline are not going to be directly affected by mean sea level change in this century (and probably not the next). What will cause major and difficult-to-predict impacts is that a hotter atmosphere will carry more water vapor (7% more water vapor for every +1 °C of atmospheric temperature) and warmer oceans with disrupted overturning circulation currents will feed more powerful tropical storms that will travel further inland and pass to higher latitudes. This will also shift precipitation patterns, leaving some areas in persistent drought will regularly inundating others with massive and sudden downpours creating flooding, erosion, damage to transportation infrastructure, and interfering with established waterways and reservoirs.
There isn’t going to be anyplace that isn’t impacted; “Climate-Proof Duluth” is a nice marketing slogan but it actually in the middle of a historical Great Plains firebelt region, and one can see that the supposedly safe Central Canada is anything but. So, wherever you live or look to move, you have to look at both individual and community adaptation measures to cope with both anticipated and unexpected climatic variations including rain and flooding, drought, powerful windstorms and tornadoes, ice storms and sudden blizzards, et cetera.
Stranger
According to that site, the climate where I live (East Midlands of England) will resemble that currently in the south of France. Which I’ve got to admit sounds pretty sweet. Major downside would be water shortages, but on the plus side, I could start a vineyard.