Modeling the Price Movement- What analysis should be used
The question is if you really want to treat this as a time series problem. I say this because there may be no obvious/persistent autocorrelation (meaning that $y$ is contingent on $y_{t-1}$).

My take (not knowing the data) would be that each hotel has an own unobserved "identity" (like location, reputation etc) apart from star rating. Bookings (and thus prices) may also be highly contingent on time. So you could give a fixed-effects model a try. The idea is that you model this in a way like:

$$y=\alpha + \beta X+\gamma Z + \theta t + u.$$

Where $X$ are observed hotel characteristics, $Z$ are hotel fixed-effects (i.e. one indicator/dummy per hotel), $t$ is time (day of year or so), and $u$ is the error term. 

In terms of model interpretation, $X$ are important (standard confounders), where $Z$ are not so relevant (and often omitted in FE regression) since $Z$ is only "one intercept per hotel". If you are interested in modeling the time aspect, clever encoding of $t$ is key. It is hard to tell how this could work out without knowing the data. There are two general options, a) dummy encoding (one dummy/indicator per time step) or continuous treatment (calender day?), maybe with a lagged component (price yesterday). In the latter case, you go in the direction of dynamic panel, which can be a little challanging. 

You can try OLS first since it is very efficient in terms of computation. In order to get a better fit you may also try boosting, e.g. based on LightGBM. Here is a minimal example for boosting regression (but no fixed-effect model, just a normal one).