You can locate the local maxima for a given radius. For example, you scan the Hough image taking peaks as maxima only when they are maximal in a $3\times 3$ window.
The second step could be refining the peak position to sub-pixel accuracy. This can be done by parabola fitting.
Suppose the value in Hough image is $f(x)$ where $x$ is the 2D position. Now you would like to find a correcting vector $p$ that maximizes $f(x + p)$. This can be written using Taylor expansion:
The correcting vector is then
The derivatives can be computed from the Hough image by finite differencing.
Note that $f''(x)$ is a $2\times2$ Hessian matrix and $f'(x)$ is a 2-vector (horizontal and vertical gradient), hence the $p$ is also a 2-vector specifying a sub-pixel shift to get accurate position of the local maximizer.
The above equation may occasionally yield shifts of more than 1 pixel. In such case, the maximizer neighborhood does not have a parabolic shape and you may not want to do the correction or should even drop the candidate maximizer.