Hello Tracey and welcome.
Your query had me busy for a couple of hours going through the directories, because the answer is far from simple.
In the first place, I have no trace of a pub named after President Wilson, but beerhouses not fully-licensed were not given names in the directories until the 1930s.
In the second place, I have found no Selina Wright to match with your census name, but there were wrights there ten years later.
In the 1869 directory, there were only a few few house numbers in Longmore Street, so it is difficult to pin the locations down, but Joseph Southam was already a beer retailer at what I think may have become 123 Longmore St.
1873: Frederick Wilkinson
1878: William Henry Winfield
1890: Alfred Benjamin Parsonage, beer retailer
1892: Henry Chinn, beer retailer
1895: George Walter Hall, beer retailer
1897: Mrs Elizabeth Wright, beer retailer
1899 Kelly's: Mrs Elizabeth Wright, beer retailer
Until this year, Longmore Street ran from Goodge Street, on the bridge over the River Rea which formerly marked the boundary between Birmingham and the old Parish of Balsall Heath, and ran across Belgrave Road to Balsall Heath Road, and the properties were numbered consecutively - starting at 1 after the bridge on the SW side running down the same side to Balsall Heath Road, then crossing over and returning on the east side to the bridge. No 123 was on the east side, roughly half way between Highgate Street and Conybere Street. But the 1900 directory, the part of Longmore Street between the bridge and Belgrave Road was renamed Gooch Street, and the houses also renumbered alternately on the whole length of the lengthened Gooch Street, so that Elizabeth Wright's address became 288 Gooch Street without her doing anything at all, certainly not moving house. The directories continue:
1900 Kelly's: Mrs Elizabeth Wright, beer retailer
1904: John Wright, beer retailer
1908: Arthur Edward Hunt, beer retailer
1913: Thomas Dodd, beer retailer
1921: James Watson, beer retailer
But by 1931, the adddress was a sub-post office, under Miss Marion E Flavell, sub-postmistress.
That's kept me going for an hour or two. Hope it is of interest to you.
Peter