- Where are the power traces?
- You can do this on a single sided board,
- Thinking ahead will give you a more practical board
- Such a big board for only 2 IC's?

I see you have conveniently made the first big beginners mistake: leave the power supply to be solved as a loose end when you're done with routing those all important signal traces, because it's only 1 big trace for 0 and 1 big trace for +5V while the real action is going on with the signals... Right?...
So maybe you can be saved while it is not too late: plan the power supply first, then worry about the signals. Yes, it's that important. Bad power supply layout is absolute champion number 1 with a vast distance when it comes to spooky problems with electronic circuits. (of course the bigger the board, the more important it gets, and if all you have ever done is small boards, you may never have encountered any problems with bad power supply layout, but just wait until you have to design a big board: it's a killer)
After the power supply, do the other important things: clock crystal, supervisor, etc. Actually, it's the data signal traces which are last in line to be put in place.

And: it is not really possible to tell from a PCB design package screenshot, but the relationship in size between the pads and the traces does not seem appropriate. Think practical, and realize that in order for you to have an eazy board to work with in practice, you will want the pads as big as possible so they don't fall off while you attempt to soder them, or they simply come off during drilling. What you should be looking for ideally is a size of pad which allows you to drill with a 0.8 mm drill (good diameter for DIP IC pins), still leave enough copper around the hole to survive drilling and soldering AND be able to run a trace between two adjacent pads like these. Because of this, an oblong pad is usually a very good choice for DIP IC's, because it fits these requirements exactly. Very practical!

With it becoming possible to run traces between two pads (which is really common practice, I'm so surprised that you don't), you will find that the design you have there will probably turn out to be possible WITHOUT A SINGLE VIA (ie: a single sided PCB). Now, I assume that you are a hobbyist, or maybe a student. Now how are you going to have your PCB design turned into a real board:
- You are going to etch it yourself in the kitchen sink,
- You have a single copy made by a professional PCB company.
In the first case, single sided boards are all you can really do well. Double sided boards are somewhat possible, but it's hard to line the component and solder layouts up plus there is no easy way of having through-hole metallized via's (and the via's you draw in your PCB design program CAN be a form of ignoring and pushing the problem ahead)
In the second case, a double sided PCB will be fully possible, but it'll cost you. Nevertheless, if you want my Eur. 0.02: don't do it in the kitchen, have it made by a company. It may cost you some, but then you save some too: a whole mess in the kitchen plus the board will be a few notches higher in quality. The trade off is more than worth it.

Also, it is best to first decide where connectors to the outside world are going to be located, before placing any components. Do not be careless about choosing the connector: don't just plop a row of dots and think "That'll probably hold a pin header"; choose a practical connector type, one appropriate for the job, and treat it as a vital component!!!!, just as you would do with the uC. Connectors are not just another loose end!!! Ask yourself if one pin row is going to be a good choice. What are you going to stick on it once you have actually built the board? How are you going to hook up the power supply? A PCB can be very convenient to work with once it's built, or it can be a nightmare of loose wires breaking off from randomly placed signal pads and pin headers. It's up to you, think about these aspects while you are at the early stages of designing the board.

I think the amount of via's you are using is excessive, and could be avoided if you would choose a pad type versus a trace width which would allow you to run traces between the pins of the IC's. There is more board space wasted on traces now than that there is going into components. You must understand that traces are really best kept as short as possible. Somehow, you must be able to come up with a tighter design than this, possibly single sided and (as I said before) one which includes a proper power supply layout from the start.