Her guitar is a Gibson Pre-'08 Les Paul Standard in Heritage Cherry Sunburst. She names it Giita, which quite literally means "guitar". In 2008, Gibson gave the "Standard" name to a new design of Les Paul, while the old Standard was renamed the Traditional; worth noting is that the manga started in 2007. She uses D'Addario EXL145 strings on it, oddly heavy strings for her and the music she plays. Of course, being Yui, she likely has no idea there are different sizes of strings, as she didn't even know they had to be changed. In the manga, its pickup selector switch is always set to the "Treble" position, which means only the Bridge Pickup is being used, which is usually well suited for lead guitar. In the anime, it's always set to the middle position, which uses both pickups, giving a more full sound, well suited for the low, Power Chord-heavy riffs Yui tends to play. Gibson's page for the Les Paul Traditional, the same guitar with a new name.
The kanji of her given name (唯) has the reading "tada", which is a word meaning "only; merely; just; simply"; as in "She is the only one who can do that." 
Yui has a habit of naming and talking to inanimate objects as if they were people, a trend that gradually includes her bandmates and their instruments. She is especially fond of her guitar, which she calls "Giita". Yui later names Mio's bass "Elizabeth" (a pun on the Japanese pronunciation of that name and the word "bass") without permission, which annoys Mio (at first). She also inspires Azusa to name her own guitar "Muttan" (which sounds like Mustang, the name of her guitar). Finally, Yui gives the name "Bukuro-chan" to the gloves Ui gave her for Christmas.
Yui is apparently allergic to air conditioning, though she can't stand overly hot or cold temperatures in general. Yui also easily gets carsick, but is immune to heat strokes. 
Yui, who is unable to write proper lyrics at first, is the one who writes Ho-Kago Tea Time's last song to be officially performed, U&I. The song is dedicated to her sister, Ui, when she realized how precious Ui is to her; Ui had caught a cold and this inspired Yui to write the lyrics. Yui also wrote Gohan wa Okazu with Ui's help.
Yui can't resist cute dogs. Every time she sees one, she holds its head and calls it cute. Her favorite breed is pugs.
Yui couldn't properly sing and play music simultaneously. Sawa-chan (Yui calls her) teaches her. Unfortunately, Yui loses her voice.
Yui has the second largest hands out of Ho-Kago Tea Time, after Mio.
Yui has a habit of hugging people when she feels like it, often without the other person's consent.
Yui can be regarded as the female counterpart to John Lennon of The Beatles. Much like Lennon, Yui is a musical prodigy despite never learning how to read sheet-music, and shares the eccentrically unorthodox yet sensitive kind and idealistic personality of his later years; not to mention the fact she, like Lennon learned how to play the guitar properly from the resident left-hander of her band, Mio (Ho-kago TeaTime's answer to Paul McCartney, whom also shares lead-vocal duties with Lennon, the idiot savant of HIS band.) Yui also openly showers Azusa, K-On!'s answer to Yoko Ono, with constant love and intimate affection. Thankfully, much unlike Lennon, she does not share the openly sarcastic, mean spirited and cynical personality of his earlier years, nor his broken and traumatic childhood, and her love for Azusa actually brought the sisterhood of Ho-kago Tea Time closer together rather than tear it apart into pieces of bitter hate the way Lennon's love for Ono did to the Beatles.
Yui could also be based on Pete Townshend of the Who (just as Ritsu bears many similarities to drummer Keith Moon 'The Loon', whom Ritsu admires). Like Townshend, Yui is a highly talented guitar player despite being almost completely self-taught and having virtually no formal training whatsoever, and she even performs Townshend's trademark 'windmill strum' on numerous occasions. Also similar is their use of Gibson guitars (although Townshend switched to Fenders in subsequent years).