Is that town property - the ditch?

The ditch, yes so i wont be planting in it id plant between the sidewalk and the ditch

Although i see others in the neighborhood who have

Given that you didn't show the whole house, it's hard to figure out how your drawing relates to the picture. I gather the water drains from both the road and the house towards the proposed rain garden site? How much water are we talking about? You'll need to do things like test how quickly water is absorbed into your soil. Rain gardens on sandy soil can be much smaller than rain gardens on clay for the same amount of water. Here are some pointers:

How to Shape a Rain Garden and Create the Right Soil for It

How to Site and Size a Rain Garden for Your Landscape

Perc test was 2.5in per hour and the road runoff will be caught by the ditch befoe it gets to the garden

The OP is very confusing as well as the title.

If you have standing water in the ditch ("culvert" is a structure), the primary reason that would happen is because the "vee" of the ditch is no longer sloped towards the direction water needs to travel. Municipalities (more often rural areas) will often regrade ditches. The second reason is blocked culverts (the pipes under the driveways). Also, from the picture it looks like the tree is in the way and was either misplanted or was an errant tree that should have been removed prior to getting too big, and the roots will have raised and changed the grade of the "vee."

Then you talk about pooling water on the sidewalk, and apparently your driveway apron slopes back towards the sidewalk according to the drawing arrows. All that needs to happen is the sidewalk and apron needs edged so the water has an area that is lower to drain to. If necessary make sure some of the parkway slopes down to the ditch, but if the water can run off the concrete into the soil, it will eventually drain underground to the ditch.

Then you talk about a rain garden, I think to be planted in the triangular area. This is not a solution to the sidewalk pooling or anything else. Where a rain garden would actually contribute, would be at the "vee" of the ditch, but that is in an easement and nothing should be planted there.