Your placement is fine.
Your routing of the crystal signal traces is fine.
Your grounding is bad. Fortunately, doing it better actually makes your PCB design easier. There will be significant high frequency content in the microcontroller return currents and the currents thru the crystal caps. These should be contained locally and NOT allowed to flow accross the main ground plane. If you don't avoid that, you don't have a ground plane anymore but a center-fed patch antenna.
Tie all the ground immediately associated with the micro together on the top layer. This includes the micro's ground pins and the ground side of the crystal caps. Then connect this net to the main ground plane in only one place. This way the high frequency loop currents caused by the micro and the crystal stay on the local net. The only current flowing thru the connection to the main ground plane are the return currents seen by the rest of the circuit.
For extra credit, so something similar with the micro's power net, place the two single feed points near each other, then put a 10 µF or so ceramic cap right between the two immediately on the micro side of the feed points. The cap becomes a second level shunt for high frequency power to ground currents produced by the micro circuit, and the closeness of the feed points reduces the patch antenna drive level of whatever escapes your other defenses.
For more details, see https://electronics.stackexchange.com/a/15143/4512.
Added in response to your new layout:
This is definitely better in that the high frequency loop currents are kept of the main ground plane. That should reduce overall radiation from the board. Since all antennas work symmetrically as receivers and transmitters, that also reduces your susceptibility to external signals.
I don't see the need to make the ground trace from the crystal caps back to the micro so fat. There is little harm in it, but it is not necessary. The currents are quite small, so even just a 8 mil trace will be fine.
I really don't see the point to the deliberate antenna coming down from the crystal caps and wrapping around the crystal. Your signals are well below where that will start to resonate, but adding gratuitous antennas when no RF transmission or reception is intended is not a good idea. You apparently are trying to put a "guard ring" around the crystal, but gave no justification why. Unless you have very high nearby dV/dt and poorly made crystals, there is no reason they need to have guard rings.
While I have to agree with the previous answers - you are indeed a lot better off in the long run if you route manually, I feel your question has not really been properly answered.
A quick-and-dirty workaround for you might be
- copy the component(s) to a library of your own
- add a new package, in which you put a GND rectangle around the entire component on the top layer only
- in the circuit, replace the original component with your tampered component
- let the autorouting commence
- go back to your circuit, and swap the component back to its original package.
Now, before the rotten-egg-throwing sets in, a few extra words why you should not do that.
While Eagle takes quite a bit of effort to get the hang of, it is definitely worth practicing these things on simple designs. As you advance, you will get to the point where you have to route manually, because some signals must be laid out in certain ways. There might still be workarounds for each specific problem, but you will never have practiced to place the components in a way that it is possible to route with minimal effort and losses.
Best Answer
It depends on the speed of your signals. Signals with really fast edges or high frequencies have different requirements. You'll need to treat them as transmission lines and control the impedance and length and everything. For slower signals, a good rule of thumb is to try to route one layer horizontally and the other vertically to reduce noise coupling like you mentioned in planes. You can also try to route all of your signals on the top layer and flood fill the bottom layer with ground copper. That will help decouple your signals and give you some extra parallel capacitance (which is a good thing). Don't be afraid to use multiple vias on the same trace if you expect higher current there. Try to avoid vias under ICs unless they're tented because you can accidentally short an IC pin to an exposed via when soldering and you won't be able to tell.