For us guys who live out in the burbs, I think we need to expand or at least refine the definition of what exactly a city block is.
If you go to wikipedia you will see that
"Since the spacing of streets in grid plans varies so widely among cities, or even within cities, it is impossible to generalize about the size of a city block. However, as reference points, the
standard block in Manhattan is about 264 by 900 feet (80 m × 274 m); and in some U.S. cities standard blocks are as wide as 660 feet (200 m). While for example, the city blocks in the central city grid of
Melbourne, Australia are 200 by 100 metres (660 ft × 330 ft)."
I think for reference points, we use New York's city block size of 264x900 feet. Now taking the 900 foot and multiplying it by 5 we get 5400 feet or approximetly 1 mile.
So If we center your home and go 1 mile in each direction that should limit the boundaries of the search.
But to be fair, since the density of the suburbs is not what the city is I think the unit of measure of a "Block" needs to change. In New York for example, within 1 city block, the number of dwellings that exist on one block may be in excess of 20-30 and some of these blocks may be multi-family or apartments and thus establishes the liklyhood of finding something interesting to have near your home location. Given density as a multiplication factor, I think we establish the fact that since we use New York's definition of a block, we also use New York's definition of the density factor and in New York, there are 71,201 residents per square mile.
So now we can put everyone on equal terms.
My town is Herndon VA which has a population of 21,378 less than that of 1/3 of a city block in New York, with an area of just over 4 square miles. Now multiplying out the the area by the density, gives me an area of interest of 12 miles.
So. Now we can find something interesting....
So equating my area of interest in Herndon VA to the Area of interest to a new york city block. I now have this area to pick from.
So in this area, my two best places would be the.
Air & Space Museum.

And
Great Falls Park.