When the alien ship disables Enterprise and flees, Archer states that the ship could be "anywhere within a half dozen light years". At warp 2 (the maximum speed of the alien ship), it would take 40 days to travel just one light year, so it had traveled almost no distance when Archer makes his statement. Even if Archer was referring to the volume of space that needed to be searched, that would be less than 2 cubic light years in a single day of travel. It has been established in other series and the Star Trek Encyclopedia that warp 2 is 10 times the speed of light, hence it would take a little over 7 months to travel 6 light years.
When in the escape pod, Tucker says that there is a planetary system 90 million kilometers away. This basically means they are already well inside the system, in our solar system a distance of 90 million kilometers from the sun would be about halfway between the orbits of Mercury and Venus.
The alien ship had a 5 month journey at warp 2. In Dead Stop (2002), it is shown that warp 2 is 9 times the speed of light, so the destination is less than 4 light years away, and Enterprise sensors have been shown to be able to detect stars and planets that close, so the destination would be obvious.
Captain Archer, when offering assistance to the freighter captain, says they "can dock in our launch bay." Unless Archer was referring to some other ship, the freighter that was shown docked with Enterprise in earlier shots is comparable in size to Enterprise itself and would in no way be able to fit inside Enterprise's launch bay, which is sized to fit shuttlepods and other small craft.