There are many ROM hacks to Super Mario Bros. that change the playable character to Peach.
Each have their own style and some make gameplay changes while most just change Mario's character to a woman.
Here is a tutorial on how to apply the ROM hack patches
A few notable ones with screenshots are:
http://www.romhacking.net/hacks/1229/
Power Peach Sis.
https://www.romhacking.net/hacks/2322/
This hack gives you the ability to play through the entire world of Super Mario Bros. as Princess Peach with her floating powers from Super Mario Bros. 2.
Created by SiWu
Funny Princess by Ultimessiah (SMB1 Hack)
Peach & Daisy - The Royal Quest (Alpha)
Super Peach (SMB1 Hack)
Created by 'Mr. Dude'
Peach's Cream
https://www.romhacking.net/hacks/986/
This ROM hack replaces Mario with Princess Peach from SMB2 and the graphics changes are from Super Mario Land. It is quite challenging.
Created by Googie.
Peach & Daisy - The Royal Games
https://www.romhacking.net/hacks/1397/
This hack allows you to play as Princess Peach or Princess Daisy in Super Mario. Some of the enemy sprites have been redesigned and all the levels have been redone.
Created by Darkdata.
Peach's Winter Adventure
https://www.romhacking.net/hacks/3602/
Girl Merio
https://www.zophar.net/hacks/nes/super-mario-bros-1/Girl-Merio-515.html
You play as a girl named Merio. Japanese text.
Girl Merio 2
https://www.zophar.net/hacks/nes/super-mario-bros-the-lost-levels/Girl-Merio-2-1039.html
Play as female version of Mario.
This is a short hack of Super Mario Bros. with Touhou Project themed graphics.
The player character is based on Touhou character, Letty Whiterock.
https://www.romhacking.net/hacks/3520/
Created by DASTARD.
Lady Opera: Swf Panic
Lady Opera was surfing the internet one day, when she found a new “Swift-brand-co”TM game!
She clicked the link and loaded the file and was sucked into the code.
Now she has to play though the game until she can find a glitch portal to escape.
https://www.romhacking.net/hacks/467/