Why didn't it ring a bell to Vader that the escape pod with the plans landed on Tatooine?
Vader was searching for the stolen Death Star plans (and in a more general sense, the location of the secret rebel base - ANH) when he intercepted Princess Leia.
Vader had no idea that Kenobi was living on Tatooine, and this thread and this thread explain how Leia knew about it and why she was sending him the plans, plus Obi-wan Kenobi was not actually part of the Alliance to Restore the Republic (Rebel Alliance).
In addition, Vader would have had no way of knowing that Tatooine was one of the destinations of Leia's ship (see note below), rather than a planet that happened to be close by when he caught up with her. In A New Hope, she states in her recording to Obi-wan that her mission to bring him to Alderaan has failed, and as she is under attack, is sending him the plans for him to bring to Alderaan. Nor is there any mention of Vader knowing from the ships logs that Tatooine was part of their itinerary, if it was even in the ships computers, especially as Leia told Vader that she was on her way to Alderaan which was technically true - she had intended to recruit Kenobi, on behalf of her father, to the Rebel Alliance.
For whatever it's worth, I'd also point out that Vader's force powers weren't all that and a bag of chips at this point since he didn't even recognise Leia when he captured her on her ship (see here and here), so he wouldn't have made the connection between Tatooine and Skywalker, and it isn't clear that the Force would have been of any help to him either. As this thread shows, at the time he didn't know of Luke being on Tatooine either.
As far as the droids go, it isn't stated that he knew C-3PO and R2D2 were the droids carrying the plans, so he wouldn't have made the connection between them (the droids he used to own, and in C-3PO's case, rebuilt) and Tatooine (where he used to live, no mention of where he was actually born). All Vader knew at the time was that he caught up with Leia, a suspected spy/rebel, near Tatooine (a poor planet of moisture farmers in the Outer Rim, an out of the way planet frequented by criminals and run by the Hutts) and in desperation she dumped the droids before they could be captured.
The points raised by @tjd and @O.R. Mapper, in the comments to this answer, are solid. Why Leia was in the Tatoo system to begin with depends on a question I could not find an answer to; namely, at what point between Polis Massa/Darknell and Tatooine, did the Tantive IV (Leia's ship) attempt to transmit the now complete Death Star plans to the Liberty? The Death Star plans were not stolen all at once, but as described in Operation Skyhook, in a series of actions that started in AX-235 or Danuta (the canon is contradictory but seems to favor Danuta), then Toprawa. The Tantive IV then moved to Polis Massa and Darknell to receive the last parts of the plans, both of which are due west of Tatooine in the 'south' the of galaxy.
I could not find in the canon where the Liberty and Tantive IV met to attempt to transfer the plans before being intercepted/interrupted by the Immortal. From there the Tantive IV and a rebel detachment moved to the Tatoo sector but their general location was betrayed by U-3PO during the Battle of Tatooine. Their specific location in the system was given away when they tried to activate an uplink station, and then Vader and his contingent moved in, leading to the capture of Leia.
The attempted activation of the uplink station still supports that Leia was again trying to transmit the plans (from an out-of-the-way location), rather than being in the Tatoo system to deliver them (which she wasn't, she was there to recruit Obi-wan). She would not have used the HoloNet as it was controlled by the Empire and she most likely could not have transmitted the plans over any large distance via hyperwave communication due its limitations, so it is reasonable that she would have dropped out of hyperspace in an out-of-the-way place to transmit the plans as securely as she could.
I have asked this as a separate question here.