I'd agree but if your etching yourself then single sided is easier, if your getting it made by a board house then vias make it easier to lay out. Out of interest do you lay out many of your own boards? I'm fairly new to this and trying to learn, but always appreciate constructive criticism.
I used to layout boards at work, it's been a couple years since I've done one though.
I still prefer to minimize vias because they can be trouble spots, especially on a high speed trace. I've had to troubleshoot more than a few boards where the problem turned out to be a bad via.
I also like to make it look nice, by that I mean I would remove excess bends and turns. Like those off of pins 2 and 3 of the IC, the dogleg going to pin 3 of the 2mm connector, the two doglegs in the traces going to pins 4 and 5 of the other connector. Pull the traces from pins 5 and 8 of the IC a little closer to the mounting hole, so that there are only 2 45's, instead of 4 in that area. And maybe push up the traces along the top so they are a little straighter (would have to see how that looked though).
I seem to recall that one should avoid traces between the long sides SMT pads, like you have between 5 & 6, but I can't remember why...
Also, you won't need the center marks for the devices, those are only used for automated assembly.
Have you checked the datasheet/appnotes to see if a bypass cap is recommended? It's pretty rare that one isn't.
If you decide to make the board single sided, it's best to assume the silkscreen won't be used either. So some marks in the copper to insure proper part orientation would be helpful. As it is now, only the 2mm connector has some way to ID pin 1.