At no time is an explicit and useful distance, time, or speed given in ANH, although a variety of numbers of limited utility show up.
However, very useful information about the nature of hyperdrive is presented in the novelization.
Solo refers to making the Kessel Run in "less than twelve parsecs," but this is also cited as "obvious misinformation" that Kenobi can see right through.
Han claims his ship can go "point five past lightspeed;" this is evidently not obvious misinformation. However, the obvious interpretation of this figure as 1.5c is not plausible. Effective FTL travel around a million system empire requires higher speeds.
To combine Han's lines, a twelve parsec trip is 40 light years, and would take almost 27 years to complete at 1.5c.
Han also says he's been across the galaxy, but this should be trusted as a literal statement no more than the other assorted "halfway across the galaxy" references found in both Star Trek and Star Wars.
Han claims that he'll have Jabba's money in "three weeks." Thus, from Tattooine to Alderaan and back cannot take any more than three weeks' round trip. Luke's training takes place entirely within the Tattooine-Alderaan run; thus, at least some hours elapsed on board the Falcon.
Setting out to Dantooine immediately before the destruction of Alderaan and after the departure of the Falcon, Imperial scouts checked the place before the Falcon arrived.
The novelization states clearly that two drives are of paramount importance - the anti-gravity drive, and the hyperdrive. FTL travel "may not occur" at the depths of a gravity well for which antigravity drive functions; thus, antigravity brings a ship out only so far, and then hyperdrive takes over. This distance may be estimated as falling between 1 and 6.5 planetary diameters for Alderaan, which may be presumed to be Earthlike - 1 planetary diameter being Han's planned exit point in Alderaan orbit, and 6.5 planetary diameters coming from the Death Star's orbit around Alderaan.
As neither point marks the beginning of a trip into hyperspace, and the novel's description indicates that both should mark the boundary, it is unclear as to which distance is the true border for hyperdrive systems. It may be the case that more powerful hyperdrives can operate deeper within a gravity well than the antigravity limit.