Downtown is not a ghost-town during the weekend... Are you serious? Basslights is going on right now in front of my building you can hear Bassnectar soundchecking haha http://www.bassnectar.net/wp-content/uploads/BASSLIGHTS2013-... And last monday we had Sigur Ros. It's all happening in the park (and other things like free yoga classes or other things I'm not into).
Or you could take the metro mover which is free (and, sadly, underused) that takes you to Brickell or north Downtown.
About Wynwood, you can avoid Overtown, using N Miami Ave or US1. My friend (who wrote this article) bikes from Midtown to Brickell a couple of times a week during the day and night.