I think you will run into some problems with this because of the location of Bethany. If you followed Jesus' last week exactly you would be running back and forwards between Bethany and the oldest parts of Jerusalem several times which is approx a couple of miles. I don't think this can be done today because Bethany is on the south-eastern side of the Mt. Of Olives in the West Bank, and it is complicated to get there because of the separation barrier. Hopefully someone local will be able to tell you if there is any possibility of getting there on foot but I don't think it is possible in the way you are looking to do this. Today, the Biblical site of Bethany is a place called Al-Eizariya (Place of Lazarus).
First of all you will find an outline of Jesus' last week here: http://www.jesus.org/death-and-resurrection/holy-week-and-passion/a-time-line-of-the-passion-week.html
Taking each day as it is there (I don't know how many days you are doing this in but you will soon see you can combine days easily.)
Sunday: I would suggest you do the traditional "Palm Sunday" walk. There is a map and description of the route here: http://www.custodia.org/default.asp?id=1886
Basically you are starting just on the east side of the Mt. of Olives and walking down past all the commemorative churches to the foot of the Kidron Valley and crossing over to St Stephens Gate on the other side. This route would be a bit less than 2 miles but it is extremely steep going down the Mt. Of Olives, the road is narrow, a few cars do go along it slowly and for safety's sake because of the steepness, you are looking at a fast walk, rather than a run. There are great some vantage points for photos of the Old City and and the oldest parts of Jerusalem on Mt. Zion near the top. Watch for pickpockets on the Mt. of Olives.
Monday: this is the same route... Stopping on the way down the Mt. of Olives at the Dominus Flevit church which was built to commemorate where Jesus wept over Jerusalem. Do go inside the church because the view from inside looking at the Old City is the spectacular view on many brochures of Israel. At the front of the church look for the tree with long spikes - this is possibly what was used for the crown of thorns.
Tuesday: same route.
Wednesday: no known route.
Thurs: Your route would start from the same place but when you cross the Kidron Valley go around the outside of the Old City to the Zion Gate. On Mt. Zion your destination is the "Cenacle" - the room supposedly on the site where Jesus ate the Last Supper. http://www.travelujah.com/blogs/entry/The-Upper-Room-The-Last-Supper-s-Cenacle-
(Note: the possible tomb of King David is at the same site so you can visit that at the same time if you wish to.)
Then go to the Garden of Gethsemane - on the lower part of the Mt. Of Olives. - maybe about a mile. From there go back to Mt. Zion to the Church of St Peter in Gallicantu. (The Church of the Cock crowing) It is thought that this may be located over Caiaphas's House and there is a dungeon there where it is possible Jesus could have been held. http://www.biblewalks.com/Sites/Gallicantu.html
Friday: This is where locations are difficult because they are mostly "traditional", might not be accurate, and so there is some guesswork on people's part. None of the locations are far apart. You would be walking through busy, streets in the Old City, and just outside to Mt. Zion.
- Trial before Annas. Some think this may have taken place at the Herodian House which they speculate may be Annas's house from objects found there. This is located in the Jewish Quarter near Hurva Square. http://www.thegospelcoalition.org/blogs/justintaylor/2012/08/28/is-this-the-high-priestly-palace-where-jesus-stood-trial/
- trial before Sanhedrin. This is thought to have possibly been a middle of the night meeting at Caiaphas's House (Church of St Peter in Gallicatu on Mt. Zion).
-third trial - at dawn. Possibly the same location?
- fourth trial - before Pilate. A possible location for this may be the Antonias fortress. I suggest your exercise in an otherwise crowded Old City day will be a run around the outside of the old city along the Kidron Valley to St. Stephen's Gate (aka Lions Gate), and that you then walk the Via Dolorosa from St Stephen's Gate. I personally don't think it is accurate, but it does go past "traditional sites" giving you time for reflection at each one. Stations 1 and two are associated with Pilate's trial. Check out http://en.m.wikipedia.org/wiki/Via_Dolorosa starting reading part way down at "Current traditional stations". Follow the route to its end at the Church of the Holy Sepulchre.
One problem with that route is the location of the 5th trial - before Herod. It is now though this could have been at Herod's Palace. I suggest you go to the Tower of David Museum at the Jaffa Gate on a separate occasion for this. If you can, do this tour: http://www.tod.org.il/en/the-kishle-and-the-citadel-moat/ It is a brand new excavation and tour (it wasn't open when I was there last year) but current thought is that this may be where the trial before Herod took place.
Saturday or Sunday: Whilst the Church of the Holy Sepulchre is probably the accurate location you should visit the "must see" site of the Garden Tomb. It's just a short walk outside the Damascus Gate and a FAR better location for reflection than the busy Church of the Holy Sepulchre. Whichever is the correct location the message is the same - the tomb is empty. http://www.gardentomb.com
I hope this is a help. Note that the Old City is only a small area, but very crowded. No place is far from another, but you could be travelling through crowded markets so you will be walking at the pace of the crowds.
Check out these pages for good info, which might help your planning:
http://www.biblewalks.com/Sites/mountzion.html
http://www.biblewalks.com/Sites/Jerusalem.html
Just inside the Jaffa Gate are some tourist information places. On the left after going through the gate there are two. The second is the official tourist info. site where you can pick up a free map of the Old City, and a leaflet on the stations of the cross. If you have a smartphone you can also download apps which give you guided tours of the Via Dolorosa etc (a local SIM card in an unlocked phone is a great help on a vacation in Israel).
You will have a wonderful trip. Enjoy! Please come back and let us know how you got on. ;)