Hi.
The Radio-Time-of-day clocks are now available for less than $30. I have seen them at Radio Shack and on line. These typically include the temperature, date and day-of-week as well as the time. The problem is, the time is in the largest characters, and the rest of the info is on the small side. Still, these can be found in really large sizes, which may give the other info in sizes large enough to read readilly, but the price goes up quickly.
I did a quick Google on "day of week clock LED project" and got several hits. I only perused the first page of hits. I found nothing immediately useful for your purposes. Still, it led to a few ideas:
1. get a microprocessor development board with an RTC (Real Time Clock) IC on it. You should be able to find articles about harnessing the uprocessor for clock projects, especially using an RTC IC.
2. purchase at least three 5x7 LED character displays. So, you can display "MON, TEU, WED, THU, FRI, SAT and SUN" for the days. If you need more clarity, purchase more of these.
3. Purchase enough shift registers (74HC(T)595) and transistors to drive all the displays, figure one each per segment. The '595 data can be found at:
https://www.ortodoxism.ro/datasheets/philips/74HC595PW.pdf
Basically you send out a long stream of bits containing the pattern info for the character displays. On the last bit you enable the outputs to actually light the displays. The transistors drive the column or row, depends on how the display is built.
You would typically use the SHIFTOUT command built into most BASICS supplied with ready built development systems, like Parallax.com's Stamp. The Parallax forums are loaded with talented people who will give lots of good advice all day. Give them a shout about your project.
I am using a board from ELProducts.com, the OEM Atom. The selling point for this board to me is the ability to program it through the serial port. No seperate programmer is needed. It doesn't have an RTC circuit, but it has a great BASIC compiler to go with it. My 'clock' uses the PIC's builtin Timer1. I have it set to run with the divide-8 prescaler. This means there's an interrupt 572 times a second. I keep adding '1' to a second's variable when the timer cycles 572 times This leads to 60 counts to count as one minute; another 60 count to count the hours; a 24 count to track the days... You get the idea. My clock is not terribly accurate, but it does pretty well. You should be able to track the days this way for several months before you have to reprogram it.
So you program in the starting time and day and start the program. Every time midnight comes you zero out the minutes and hours and display the new day. You need to store the patterns for the letters in the names of the days. You use the SHIFT command to send these out to the registers that drive the segments of the display, You use other pins of the processor to drive the transistors.
'Hope that helped! Good luck on your project.
kenjj