Rayiner has already pointed out that Austin is not in the so-called plaintiff friendly Eastern District of Texas (EDT).
Also, it's not clear that EDT is actually plaintiff friendly. Defendants win plenty of cases there, and last time I saw stats it didn't seem particularly outstanding. There were several that had significantly higher plaintiff win rates. The numbers can change dramatically from year to year, though, so what I saw may be outdated.
(Update: 2016 plaintiff won 36% of patent trials in EDT. 2015 was 50%, 2014 was 67%, and 2013 was 33%. These are lower than the overall national plaintiff patent win rate, I think [1] [2] [3]).
A big reason plaintiffs choose EDT is that it is fast and experienced (the former partly due to the latter). Patent suits are civil cases heard in Federal district courts. Federal district courts also deal with criminal cases, and criminal cases have higher priority.
In some districts where there is a heavy load of criminal cases the civil cases can end up move very slowly. EDT doesn't have much crime, so there aren't many criminal cases there. They have plenty of time for civil cases.
Patent cases are among the more technically complicated cases. They will go a lot smoother if handled by a judge who is experienced with them. Once a judge gets experience with a few patent cases, that can attract plaintiffs to that district. Some judges like patent cases, and so whenever one is filed in the district they serve in, they ask to have it assigned to them. That in turn makes the them even more attractive to future plaintiffs.
Patent cases are often "big". What I mean by that is that they often involve a lot of people attending the trial or accompanying those who attend the trial. Each party will have patent lawyers (often more than one) and trial lawyers (often more than one) on their team. Those will all have secretaries and paralegals. They will have witnesses, which on the plaintiff side will at least include the inventor(s) and probably others who were involved with the invention, and on the defendant side will include the people who developed the technology that defendant used that is accused of infringing. There will be expert witnesses both sides have hired to explain the patent and the technology, both as used by plaintiff and by the accused infringer. Both sides will also probably have a damages expert. Both sides will have rented at least one large conference room at their hotel, and will have brought along an IT team that will arrange high speed internet in that conference room and have set it up as a nearly complete office, complete with workstations, printers, phones, FAX, and so on. There will be a multimedia team that makes graphics and animations for presentation during the trial.
The trial itself might last a week or two, but most of the above team will be there for two to four weeks before the trial starts. What that means is that you might be looking at needing 30ish hotel rooms, plus a big dedicated meeting room, and probably several smaller dedicated meeting rooms, for four to six weeks, and you want this reasonably close to the court.
Keep in mind both sides are doing this, so you are looking at 60+ people staying at good hotels, renting expensive meeting facilities, using the services of many local businesses (restaurants, car rental, office equipment rental, cleaners, clothing stores, barbers and stylists) for a month or more. This can bring in a pretty good amount of money to the local economy.
District judges generally live in the districts in which they serve, and are aware that these big cases are good for their districts. They sometimes take steps to encourage such cases to come to their districts, such as adopting local rules to make handling particular types of cases more efficient. EDT has done that with patent cases. I recall reading of a few other districts that do similar, but for specialities other than patents, but cannot recall specifics.
[1] http://mcsmith.blogs.com/eastern_district_of_texas/2016/08/2...
[2] https://www.pwc.com/us/en/forensic-services/publications/ass...
[3] https://www.thenaplesroundtable.org/wp-content/uploads/2016/...