If you have an afternoon to spend around Athens, a walk around Monastiraki and Plaka is a pleasant experience. Best time to start would be around 7:30 or 8:00 PM, after the sun has journeyed close or beyond the horizon line and the daylight heat begins subsiding.
The total distance of this walk is about 2.5 kilometers (1.5 UK/US miles).
Start at Syntagma square where you can spend some time people-watching. Many tourists would venture across the busy street to feed the pigeons and to watch the changing of the guard at the tomb of the unknown soldier in front of the Parliament. The most adventurous ones would take their souvenir photo standing next to the immovable statuette guards, especially those who find the traditional military uniform noteworthy. It doesn't hurt that the presidential guards sport a bayonet-fixed weapon, pom-pom shoes, stockings, and a pleated mini skirt (photo of the Syntagma presidential guards here). Never mind that the outfit was developed for agility in the mountainous terrain of Greece, more than a century before the fashionable skirts scandalized puritans in the 1960's.
Behind the Parliament is the extensive National Gardens. If you have a lot of time to kill, you can wander through its paths, but if you've been in other parks in Europe or in the US, it will not be very interesting, and it is by no means a quiet place for a stroll.
From Syntagma square, take Ermou west towards Monastiraki. To find Ermou, stand in front of the fountain in the middle of the square keeping the Parliament to your back. The street right in front of you is Ermou. Most of the shops sell fashion items, apparel, and electronics, but soon the street will take you to the ancient church of Panagia Kapnikarea, and a few blocks after that, you will reach the full of life square of Monastiraki.
Make a left onto Mitropoleos, and enjoy a leisurely walk flanked by restaurants most of which offer gyros and grilled meats. Mitropoleos quickly will bring you to Mitropoleos square where you will be confronted with the stately Cathedral (Mitropolis) of Athens. While large and imposing, it's not the most important church in the square. Right next to it, don't miss the beautiful and historic Agios Eleftherios church. What the little church lacks in size, makes up with it's beautiful proportions and elegant silhouette and decorative details. Look closely and you will see many marble stones embedded in it's walls, most of which came from the Acropolis at a time when it was considered to be a convenient quarry of stones for the authorities of the (then) new order. The restaurants on Mitropoleos square are on the expensive side of life, but having a frappé might not be a bad idea if you are tired. If you can still walk, keep moving.
From the front of the little church (with the church on your back) walk straight to Pandrosou to enjoy a purely "touristy" experience though all the little souvenir shops and the wandering visitors. It would only take a few pleasant blocks to bring you back to Monastiraki square. Cross the square, and continue onward to Ifaistou thrift shops.
It's not easy counting "blocks" in these pedestrian streets, but about five blocks ahead, make a left on Kinetou street to reach Andrianou in front of the archaeological site of the Agora.
Make a right on Andrianou and survey the restaurants and cafés lining the street, knowing that there are more restaurants behind you and that your meal would be mostly memorable for the view of the ancient sites. Try to be polite when you fen off the waiters who try to entice you to sit at their own restaurant and soon you will find the street becoming wider and splitting in front of the Thesion metro station. The first impulse is to turn back and walk through Adrianou again, but if you are up for a longer stroll, continue to your left through Ilia Pouliopoulou street, lined with jewelry and other artisan kiosks.
Within minutes, you will find yourself on a wider pedestrian street called Apostolou Pavlou. The coffee shops that flank the street are frequented mostly by Greeks, but soon you will find yourself in smaller and smaller crowds as you move toward the Acropolis entrance.
The road will split right at the path that takes you up to the Acropolis, and you should take the wide path to your left (not the one up the hill) called Dionysiou Aeropagitou. Within five blocks you will reach the imposing Acropolis Museum and a host of street vendors and performers in front of it.
Make a left after the museum onto Vyronos street and you'll be walking in Plaka and winding old streets again. Make a right on Lysikratous, and then a quick left onto Andrianou street.
Adrianou street is packed with shops and restaurants and it will take you back to Monastiraki square where you can hop on the metro back to your hotel.
Don't forget to take time to do some shopping, to enjoy the street life and a good meal whenever it seems appropriate. There are plenty of places to do all that in every corner. Power walking is not out of the question but these streets are more conducive to a leisurely stroll than an exercise session. If you are in need of a bathroom you can use any cafeteria, although more moder-looking cafés are the better options and you can often walk right through to the restroom without asking.