Lane-free traffic environments allow vehicles to better harness the lateral capacity of the road without being restricted to lane-keeping, thereby increasing the traffic flow rates. As such, we have a distinct and more challenging setting for autonomous driving. In this work, we consider a Monte-Carlo Tree Search (MCTS) planning approach for single-agent autonomous driving in lane-free traffic, where the associated Markov Decision Process we formulate is influenced from existing approaches tied to reinforcement learning frameworks. In addition, MCTS is equipped with a pre-trained neural network (NN) that guides the selection phase. This procedure incorporates the predictive capabilities of NNs for a more informed tree search process under computational constraints. In our experimental evaluation, we consider metrics that address both safety (through collision rates) and efficacy (through measured speed). Then, we examine: (a) the influence of isotropic state information for vehicles in a lane-free environment, resulting in nudging behaviour--vehicles' policy reacts due to the presence of faster tailing ones, (b) the acceleration of performance for the NN-guided variant of MCTS, and (c) the trade-off between computational resources and solution quality.