@ted_scott
I assume in 1960 a massage would have been $10 or less, (I remember my first job in 1970 paid minimum wage which had just gone up from $1.40 to $1.60)
There are quite a number of variables to be considered.
Location in the USA is a major consideration. Several cities in California have a "China Town" San Francisco, and Los Angeles most prominent; probably San Diego, but that is an uncommon "blank" in my knowledge of history in general and of Asian immigration to the USA in particular. New York City and several other major port cities in the USA also have a "China Town"; in Seattle it was a "Japan Town" at least until 1942 and POTUS Roosevelt had many people of Japanese ancestry rounded up and put in concentration camps. Salt Lake City has a "China Town" because thousands of workers on the Transcontinental Railroad were laid off in Utah when the west and eastern links were connected.
Portland, Oregon had AMPs in the 1960's, but not a "China Town" per se; but for various reasons had (and has) strip clubs and massage parlors.
Near many major US Army, Navy, and Marine bases there were AMPs since the mid 1950's in the aftermath of the "hot" period of the conflict in Korea (officially a "police action" "not" a war). {Air Force bases were either collocated near Army bases, or much smaller, thus a significantly smaller customer base for an AMP; as well as tolerance of the local population/Politicians/law enforcement authorities.}
Fort Lewis (just south of Tacoma, and Seattle), Fort Ord (north of LA), Fort Benning, Georgia, Fort Bragg, NC (and Camp Lejune also in NC), and Camp Pendelton in southern California. These are the bases where it was typical for soldiers/Marines to go to/come from Japan/South Korea/ Vietnam; etc. Likely there were AMPs in Denver; but I doubt they were in Pueblo, CO in the 1960's despite the proximity of Fort Carson. Similarly unlikely in Manhattan, KS adjacent to Fort Riley. Fort Dix was primarily a Basic Training facility.
Racism made the tolerance for AMPs outside of a China Town (or the unofficial "Red Light District" near the gates of some major military/naval bases) was problematic. The public, thus Politicians who set law enforcement priorities did not tolerate visible prostitution, such as AMPs except in extremely limited locations/circumstances. Prostitution in most cities was controlled, or at least under the "protection" of organized crime that in the 1960's was dominated by the various Italian (mostly, but not always Sicilian), or Irish, or Jewish "Mobs" (other ethnic groups also had organized crime, but those are limited to very specific locations and circumstances; further they were far less likely to have clients outside their ethnic base). Las Vegas, and the rest of Nevada had (and still have) restrictive laws against prostitution; at least something as "visible" as an Asian Massage Parlor.
Which Asians are in the Asian Massage Parlor? Or rather, which nationality is Controlling the AMP? By the 1960's there would be very few, if any Japanese women in an AMP (except for secret ones for {almost} exclusively Japanese clients); Japanese organized criminals might control an AMP, but that would be uncommon; except for some specific locations. Chinese would be the most common ethnic group to operate an AMP, and would also be the most common females employed. Koreans might be employed in an AMP run by either Chinese or Japanese. In the 1960's it would be very rare to for Vietnamese, Thais, or other Asians to be employed in an AMP; let alone operate one.
Prices would vary a lot based upon the clientele, and to a lesser degree region of the USA. Unless they are "slumming" wealthy people would not patronize an AMP. "Middle Class" businessmen in NYC, LA, or SF, would typically go to a nicer location with higher operating costs. (Similar to Mad Men, most upper and middle class businessmen would have encountered an AMP during Occupation Duty in Japan or South Korea; or on leave from South Vietnam {in Bangkok or elsewhere}.) Soldiers, Sailors, and Marines would have significantly different pricing points than businessmen.
Prices would take a significant jump between 1963 and 1969.
As an extremely general SWAG for a "Blue Collar" (military/naval clients too) would be $5 to $15 for 30 minutes to 60 minutes of a massage.
For a Handjob, the most common "Happy Ending" I would expect $10 to $25 depending upon a plethora of factors (economy, location, if a customer is a "Regular" how the customer presents when they arrive at the AMP).
A "tit-job" (perhaps + oral) would be the next probable; but likely only after multiple visits with only a HJ HE. Less likely, but possible at "higher end" AMPs might range from $15 to $50.
Oral sex might be obtainable, but with even more variable that a TJ; and in a similar price range.
Fucking, for most White men would be unlikely, but possible. It would probably require a condom, which is potential Evidence if the AMP is raided! Thus, unless the person who operates the AMPP is confident they won't be raided by the Vice Squad, "Full Service" aka fucking is unlikely; except for "special" customers. Price has numerous variables, but perhaps $50 to $100.00. Remember this is the era of Blue Laws!
Black men and Latinos (except for some who would be considered "White") wouldn't be able to patronize an AMP; except, possibly, for service members at some AMPs adjacent to a base. Perhaps, with a "reference" from a regular client, it might be possible for a Black man to get services at an AMP. Unlikely, but possible.