Count number of hours elapsed
A few comments to start with:-


The 4511 needs unused inputs tied to an appropriate logic level
The 4511 needs series resistors on each of the segment outputs to the common-cathode display
You are using museum-quality TTL, so you should have a pull-up on the RESET input and pull it down to ground with the switch. 
One day (Edit: or one hour) is not a reasonable period to get from a 555 (even a CMOS one). Keep it to 1-10 seconds. The leakage on a 0.1F capacitor would make a mockery of your precise calculations. You can count down a higher frequency if you like. A 74HC4040 prescaler would allow a ~1 second clock. 
You'll never get better than maybe 5% without adjustment on a 555, and even if you trim it, tenths of a percent. That may not bother you, but the count might be off by an hour in ten or twenty without trimming. Think of how many weeks(Edit: days) it would take to trim a timer with a 1-day (Edit: or one hour) cycle! 
I don't know what a 7469 is.. something like a 74390 dual decade counter perhaps? 
10uF is unnecessarily high for the control bypass- 100nF is more than enough. 
I didn't check your logic (the semi-pictorial is a bit painful to read) but it looks plausible as a plugboard starting point.