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The Time Lord in Terror of the Autons says he has travelled 29,000 light years, which is about the distance from Earth to the centre of the Milky Way. Assuming he's come straight to Earth, this would indicate that Gallifrey is at the galactic core, or very far out on the edge, or above the plane of the galaxy. The first assumption seems the most reasonable.
In Marco Polo, Susan tells Ping Cho that her home is 'as far as a night star', which, if taken literally, means that it's in Earth's galaxy. Gallifrey's star lies within the constellation of Kasterborous, as seen from Earth (see Mission to the Unknown). The galactic core is in Sagittarius, so perhaps Kasterborous occupies the same area in Earth's sky in the future. In Pyramids of Mars Gallifrey is said to have the binary coordinates of 1001100 by 02 (in Gallifreyan notation only the first part is binary). Gallifrey is a few billion millions away from Karn, putting it in the same solar system, with at least three other planets (The Brain of Morbius), possibly four (The Deadly Assassin).
If Gallifrey is in the Milky Way then 'Mutter's Spiral' is either the Time Lord name for our own galaxy or a reference to the galaxy's spiral arms (they being at the core). Another name for Earth's galaxy is the Stellian Galaxy (The Trial of a Time Lord). The centre of human affairs, some centuries in the future, moves to the galactic core (The Happiness Patrol), which might give Gallifrey pause for thought.