Parking areas will be all over outside the historical centers of all those towns. Anghiari has several above and below the historical center.
Follow the directions to the city center. In Italian that is CENTRO or CENTRO CITTA'. The sign will be white with the city center logo which is similar to a target symbol (just like the Target store logo, but black instead of red). As you get close to the city center look for the signs to the parking lots. Parking lots are marked by the sign below.
https://commons.m.wikimedia.org/wiki/File:Italian_traffic_signs_-_parcheggio.svg
I don't remember if there are areas in the historical centers you mentioned that are prohibited to non residents' vehicles (Cortona does have a ZTL so watch out). But even in the historical centers where access is permitted, parking may not be (or it will be simply unavailable due to lack of space) except for the designated parking lots marked by the P sign above.
I must make some clarification to Jim's comment. What he writes is incorrect. Blue stripes mean indeed pay parking. Yellow stripes however is NOT residents parking, rather it is RESTRICTED parking to categories of vehicles as specified by the sign (handicapped parking, police vehicle, taxi, bus, etc.).
White stripes are tricky. It could be free unrestricted parking or also residents' only parking. That distinction will be specified on the signs. Therefore when you see white stripes don't necessarily assume you are ok.
The safest parking is always in the parking lots indicated by the sign linked above. If the stripes are blue, you need to pay something at the parking meter machine (and put the parking receipt on the dashboard), if the stripes are white, it's free.
Also pay attention to limited hourly parking areas (for example 2 hours max). They are free but they might say DISCO ORARIO and indicate the max hours you can park. That is similar to the time restricted parking in the US (like 2 Hr parking), where the parking maid comes and marks your tires with a chalk. In Italy the police uses no chalk. All cars (including your rental) will have a DISCO ORARIO (like a paper clock). Just rotate it to indicate the time you arrived. Make sure you return timely. When the police comes to check, they will look at the time of arrival you marked. If you are parked passed the time you are allowed, you get ticketed. Cheating by marking the time of arrival after your actual time of arrival (to gain some extra time) doesn't work. If the police arrives before the time you marked you arrived they will ticket you.
Below is an example of a sign for DISCO ORARIO parking limited to 1 hr between 8:00 and 20:00 hours.
http://www.agorabrenna.it/arch/stb/?p=904
This is how the disco orario on the windshield of your rental car might look (there are many designs).
http://www.altarimini.it/misano_raddoppiano_le_ore_a_disco_orario_30545.php