I was looking for a multifamily, but the ones available were in declining neighborhoods.

HOA and property management are the biggest declines to the cash flow. 

Is the neighborhood declining or improving?

https://www.har.com/content/newsroom/Houston Real Estate Highlights in May, 2023:-Single-family home sales were down 10.4 percent year-over-year, the 14th consecutive month of slowing sales volume but the lowest rate of decline since June 2022, suggesting that improved market conditions may be looming;-Compared to pre-pandemic 2019, single-family home sales were down just 1.3 percent, however they were up 6.4 percent versus the volume five years ago, in May 2018;-All housing segments experienced sales declines except homes priced below $100,000; -Days on Market (DOM) for single-family homes rose from 30 to 48 days;-Total property sales fell 12.5 percent with 10,476 units sold;-Total dollar volume dropped 12.7 percent to $4.3 billion;-The single-family median price dropped 3.1 percent to $340,095;-The single-family average price fell 1.6 percent to $431,378; -Single-family home months of inventory registered a 2.8-months supply, up from 1.5 months a year earlier;-Townhome/condominium sales experienced their 12th straight monthly decline, falling 26.1 percent, with the median price down 6.0 percent to $216,300 and the average price down 3.7 percent to $262,015;-Compared to pre-pandemic 2019, townhome and condominium sales were down 7.7 percent.

Do they ever decline an application for a STR permit?

For example, if you get the feeling that a certain tenant will be very needy during their tenancy - calling you for lightbulb changes or because the neighbour closed their car door too loudly - then it's ok for you to decline their application even though there is nothing 'wrong' with their application. 

I have a friend who bought a new town home in the area a few years ago, only to see the value decline as more riff rafts moved into the neighborhood.

May is traditionally higher price than January, so clearly it is less than 8% decline but the true decline may not be known until May. 

This involves analyzing data to determine whether the neighborhood is experiencing growth or decline in terms of population, job opportunities, and other economic factors.

The area is in decline, not growth.