Then get a dog to run with you. Statistics show that running with a dog, (even a small dog), really improves safety for women runners. I run every day with my German Shepherd and feel really safe!!!!
Midtown, Land Park, and Curtis Park are also close to downtown--and all have particular sections that are considered desirable and safe. I just don't know those areas well enough to say where.
I'd avoid downtown proper. It's just fine during the workday, but it's pretty deserted evenings and weekends, and not somewhere you'd want to be hanging out by yourself.